It is a verb in British English: commentate: VERB
[NO OBJECT] British Report on an event as it occurs, especially for a news or sports broadcast; provide a commentary. https://en.oxforddictionaries.com/definition/commentate
ell.stackexchange.com/users/59859/Keith McClary
Running commentary is also fairly common.
running commentary ( noun ) a continuous spoken description of an event while it is happening
ell.stackexchange.com/users/96768/snugghash
The classic phrase for such a description is play-by-play .
Literally this means a detailed description of a sports event, describing each event in the game as it happens.
But it has been extended to descriptions of other sorts of events, including political ones, on a similar as-it-happens basis.
Such "play-by-play" descriptions arose when games were broadcast by radio, with no accompanying images, because video had not yet been developed.
The intent was to give the listeners the same information as they would have if they were physically present.
Indeed it gave more, because the broadcaster often had expert knowledge of what to watch for, what was significant, that many people did not have, or not to the same degree.
It is also known as "play-by-play commentary."
Strictly speaking the commentary is the account of the event, not the process of delivering that account, but it is often extended to cover the process as well.
The action of doing the description is sometimes called "giving a play-by-play" or "delivering a play-by-play".
In either case, "commentary" can be added.
ell.stackexchange.com/users/91457/David Siegel
Commentary is the noun, but as you are asking for the action, the corresponding verb is commentate/commentating .
Those who commentate are called commentators
ell.stackexchange.com/users/8790/curiousdannii
There's narrating verb (used with object), nar·rat·ed, nar·rat·ing. to give an account or tell the story of (events, experiences, etc.). to add a spoken commentary to (a film, television program, etc.) or cast In sports broadcasting, a sports commentator (also known as sports announcer, sportscaster or play-by-play announcer) gives a running commentary of a game or event in real time, usually during a live broadcast, traditionally delivered in the historical present tense.
This is used a lot regarding games, such as on Twitch,
although there it can be used very broadly: often someone casting a game will be discussing things only tangentially, if at all, related to the game.
Also, while the traditional past tense of "cast" is just "cast", many people now use "casted".
ell.stackexchange.com/users/61500/Acccumulation
If it specific to sports, as the other answers have said, commentating or running commentary is the common word.
Reporting live is another which I think has a broader potential context of use.
Also, reporting tends to be more about the events with as little 'extra information' as possible, while commentary tends to include some opinion or any other relevant extra information.
ell.stackexchange.com/users/96883/Emmanuel
In British English, "live commentary" is probably the most common phrase for this.
For example, the national UK radio station that specialises in sports reporting uses it in its schedules .
ell.stackexchange.com/users/37000/Especially Lime
A less common phrase would be " color commentary ", referring particularly to background information provided between plays.
ell.stackexchange.com/users/96738/stephan.com
"Calling the game" can also be used.
The same term gets used in place of "calling off the game" (e.g. due to rain), but there's plenty of references as to it being used to denote commentating.
ell.stackexchange.com/users/96859/user96859
One answer that I haven't seen here yet is "Casting".
A especially eSports, a lot of the announcers call themselves casters, and I've heard the term use in ways like "sports casting".
ell.stackexchange.com/users/96894/Noah
What do you call the action of "describing events as they happen" like sports anchors do? I heard the word "commentary", but I doubt "commentary" actually refers to the action of describing an event as it's happening. Also, I am wondering what the verb might be.   Here's a video example, but I doubt it's needed:  https://www.youtube.com/watch?v=iiYXiRZncYk
What do you call the action of "describing events as they happen" like sports anchors do?
ell.stackexchange.com
<word-request>
ell.stackexchange.com/questions/214076
ell.stackexchange.com/users/93377/blackbird
Running commentary  ( noun ) a continuous spoken description of an event while it is happening.   In British English, "live commentary" is probably the most common phrase for this.  The possibilities are: "providing a commentary, a running commentary or a live commentary. Moreover, one other option that can be used is casting. 
The possibilities are: "providing a commentary, a running commentary or a live commentary. One other option that can be used is casting. 