I would use a 1" diameter straight cutting bit on a router table to make the main compartment body.
You'll have to raise it up into the workpiece to avoid having an open end on the compartment though.
For the slot, you can just use a slot cutting bit or set with a bearing guide to follow the edge around.
If you think you'll have clearance issues with the bearing and nut, you could always get a top-bearing slot cutter instead.
woodworking.stackexchange.com/users/38/Doresoom
This could be easily cut with a T-Slot Router bit
woodworking.stackexchange.com/users/11/Steven
I did a little search and found ISCAR has a set of T bits that can cut slots from 2mm - 5mm.
The cutting end can be removed and replaced with different thickness cutters giving you the option to have many different sized slots with one bit.
Though after further looking it is really designed for metal cutting, it might work.
http://www.iscar.com/Products.aspx/CountryID/1/ProductId/10155
I've seen several others and most seem to be for cutting metal and none seem very cheap.
Another option might be to use an angled router bit like those for dovetails.
Then you can make a piece like a wedge and slide it in.
woodworking.stackexchange.com/users/27/bowlturner
It looks almost like it would require a Dremel tool
The slot that holds the compartment cover looks too narrow to be cut by any router bit that I've seen, and I agree that something like a Dremel tool with a fine saw blade could do the trick.
Another way to approach the problem is to remove the back of the board, form the slot, and then replace the back: Rout the compartment.
Slice the back of the board off with a band saw.
Rout out the area around the compartment using a bit depth that matches the slot width.
Glue the back of the board back on.
I know this might sound like a crazy idea, but if you have a good sharp resaw blade in the bandsaw the glue joint practically disappears.
People who aren't looking for it will never notice.
woodworking.stackexchange.com/users/492/Caleb
They probably used a small slotting bit in a router table, or something similar.
Of course there's nothing that requires using that particular compartment design...
woodworking.stackexchange.com/users/91/keshlam
I'm making a peg cribbage board and want to make a peg compartment with a sliding door.   It looks almost like it would require a Dremel tool, but was wondering if anyone has any techniques for accomplishing the task.
How can I make this cribbage board peg compartment?
woodworking.stackexchange.com
<technique>
woodworking.stackexchange.com/questions/1570
woodworking.stackexchange.com/users/652/Troy
Use a  1" diameter straight cutting bit  on a router table to make the main compartment body of the cribbage peg board. Alternatively, a Dremel tool is recommended. A slot cutting tool is recommended for the slots. A router bit is widely recommended. However, a dremel tool with a fine saw blade may be the best option.
A router bit is widely recommended. A dremel tool with a fine saw blade may be the best option.