user18029: Chess is used as an example of how the body can be influenced purely by brain activity:

In the middle of a chess Grand Master tournament these people are maintaining blood pressure for 6 hours' running that you only see in a marathon runner


These people are going through thousands of calories per day doing nothing more than thinking

and even that:

one of these chess Grand Masters who's just taken down an opponent ... has the exact same physiology as some ... baboon on the Savanna who's just ripped the stomach open of his rival!

Also note, it's mentioned here that Fischer was

built like an olympic athlete

In terms of heart rate, breathing, energy consumption ('calories'), and other biometric indicators, what are the typical physiological responses of the human body to an important, high-level classical chess game?

user17203: The video in the original question featured Robert Sapolsky, also author of Why Zebras Don't Get Ulcers, who famously has said that a grandmaster can burn 6000 calories in a day of chess. I believe the following is from Sapolsky's book:

The definitive study on chess players was carried out by the
physiologist Leroy DuBeck and his graduate student Charlotte Leedy.
They wired up chess players in order to measure their breathing rates,
blood pressure, muscle contractions, and so on, and monitored the
players before, during, and after major tournaments. They found
tripling of breathing rates, muscle contractions, systolic blood
pressures that soared to over 200—exactly the sort of thing seen in
athletes during physical competition.
See the original report, Leedy’s thesis, “The effects of tournament
chess playing on selected physiological responses in players of
varying aspirations and abilities” (Temple University, 1975) or their
brief report (Leedy, C, and DuBeck, L., “Physiological changes during
tournament chess,” Chess Life and Review [1971]: 708).
In a telephone conversation, DuBeck also tells the story of the
international match in the early 1970s between grand masters Bent
Larson and Bobby Fischer, in which the former had to be given
antihypertensive medication in the middle of his losing match; his
blood pressure remained elevated for days afterward.
The Kasparov-Karpov report is from the New York Times, 20 December
1990. And for that special chess fan out there who just can’t get enough of this subject, may I suggest as the perfect gift a copy of
Glezerov, V., and Sobol, E., “Hygienic evaluation of the changes in
work capacity of young chess players during training,” Gigiena i
Sanitariia 24 (1987), in the original Russian.

I got the above from Christoffer Torris Olsen's answer to Does playing chess burn as many calories as running? on [skeptics] Stack Exchange.

user27533: European Journal of Applied Physiology studied the physiological consequences of the tension caused by playing chess in 20 male chess players, by following heart rate, heart rate variability, and respiratory variables. We observed significant increase in the heart rate (75-86 beats/min), in the ratio low frequency (LF)/high frequency (HF) of heart rate variability (1.3-3.0) and also a decrease in mean heart rate variability with no changes in HF throughout the game. These results suggest a stimulation of the sympathetic nervous system with no changes in the parasympathetic system. The respiratory exchange ratio was rather elevated (over 0.89) at the start and significantly decreased during the game (0.75 at the end), indicating that energy expenditure progressively switched from carbohydrate to lipid oxidation. The changes in substrate oxidation and the sympathetic system seem to be due to high cognitive demands and bring new insight into adaptations to mental strain.

18029: <p>Chess is used as an example of <a href="https://www.youtube.com/watch?v=NNnIGh9g6fA#t=37m03s" rel="noreferrer">how the body can be influenced purely by brain activity</a>:</p>
<blockquote>
<p>In the middle of a chess Grand Master tournament these people are maintaining blood pressure for 6 hours' running that you only see in a marathon runner</p>
</blockquote>
<blockquote>
<p>These people are going through thousands of calories per day doing nothing more than thinking</p>
</blockquote>
<p>and even that:</p>
<blockquote>
<p>one of these chess Grand Masters who's just taken down an opponent ... has the exact same physiology as some ... baboon on the Savanna who's just ripped the stomach open of his rival!</p>
</blockquote>
<p>Also note, it's mentioned <a href="https://www.youtube.com/watch?v=oSyMmleisQM#t=20m42s" rel="noreferrer">here</a> that Fischer was</p>
<blockquote>
<p>built like an olympic athlete</p>
</blockquote>
<p>In terms of heart rate, breathing, energy consumption ('calories'), and other biometric indicators, what are the typical <a href="https://en.wikipedia.org/wiki/Physiology" rel="noreferrer">physiological</a> responses of the human body to an important, high-level classical chess game?</p>
 17203: <p>The video in the original question featured Robert Sapolsky, also author of <em><a href="https://rads.stackoverflow.com/amzn/click/com/0805073698" rel="nofollow noreferrer" rel="nofollow noreferrer">Why Zebras Don't Get Ulcers</a></em>, who famously has said that <a href="https://www.youtube.com/watch?v=hrCVu25wQ5s#t=10m04s" rel="nofollow noreferrer">a grandmaster can burn 6000 calories in a day of chess</a>. I believe the following is from Sapolsky's book:</p>
<blockquote>
<p>The definitive study on chess players was carried out by the
physiologist Leroy DuBeck and his graduate student Charlotte Leedy.
They wired up chess players in order to measure their breathing rates,
blood pressure, muscle contractions, and so on, and monitored the
players before, during, and after major tournaments. They found
tripling of breathing rates, muscle contractions, systolic blood
pressures that soared to over 200—exactly the sort of thing seen in
athletes during physical competition.</p>
<p>See the original report, Leedy’s thesis, “The effects of tournament
chess playing on selected physiological responses in players of
varying aspirations and abilities” (Temple University, 1975) or their
brief report (Leedy, C, and DuBeck, L., “Physiological changes during
tournament chess,” Chess Life and Review [1971]: 708).</p>
<p>In a telephone conversation, DuBeck also tells the story of the
international match in the early 1970s between grand masters Bent
Larson and Bobby Fischer, in which the former had to be given
antihypertensive medication in the middle of his losing match; his
blood pressure remained elevated for days afterward.</p>
<p>The Kasparov-Karpov report is from the New York Times, 20 December
1990. And for that special chess fan out there who just can’t get enough of this subject, may I suggest as the perfect gift a copy of
Glezerov, V., and Sobol, E., “Hygienic evaluation of the changes in
work capacity of young chess players during training,” Gigiena i
Sanitariia 24 (1987), in the original Russian.</p>
</blockquote>
<p>I got the above from <a href="https://skeptics.stackexchange.com/a/14174">Christoffer Torris Olsen's answer</a> to <a href="https://skeptics.stackexchange.com/questions/7527/does-playing-chess-burn-as-many-calories-as-running">Does playing chess burn as many calories as running?</a> on [skeptics] Stack Exchange.</p>
 27533: <p>European Journal of Applied Physiology studied the physiological consequences of the tension caused by playing chess in 20 male chess players, by following heart rate, heart rate variability, and respiratory variables. We observed significant increase in the heart rate (75-86 beats/min), in the ratio low frequency (LF)/high frequency (HF) of heart rate variability (1.3-3.0) and also a decrease in mean heart rate variability with no changes in HF throughout the game. These results suggest a stimulation of the sympathetic nervous system with no changes in the parasympathetic system. The respiratory exchange ratio was rather elevated (over 0.89) at the start and significantly decreased during the game (0.75 at the end), indicating that energy expenditure progressively switched from carbohydrate to lipid oxidation. The changes in substrate oxidation and the sympathetic system seem to be due to high cognitive demands and bring new insight into adaptations to mental strain.</p>
