SOLUTION: BEE-ROLLANSWER: HEAD LOCK
The description of the bees' game is straightforward, but the names of the eight players are not given. The easiest first step toward discovering the theme of this puzzle is by searching the phrase "Hello bees!", a greeting shouted by the character Jester Lavorre in a notable scene in the "Mighty Nein" campaign of the actual-play TTRPG show Critical Role. (The word "mighty" in the game description, the shape of the table matching the actual Critical Role table, and the word "critters" in the flavortext ("Critters" being a term used for Critical Role fans) all provide confirmation that Critical Role is the franchise in question. Here is the standard seating chart for the Mighty Nein table, as can be deduced from various gameplay footage:
It isn't specified whether the cast members' or their character's names are needed, but the enumerations in the given diagram confirm that the first names of the characters are used, additionally disambiguating which of Taliesin Jaffe's characters is needed (as Caduceus is the only eight-letter name of his Mighty Nein characters). This is also reinforced by Dungeon Master Matthew Mercer being given the title of "The Bee with Many Names", as he primarily is responsible for playing the non-player characters on Critical Role. The details of the bees' game are trivial once the names are identified:
1. JESTER rolls a 3, steals L from CALEB
2. CALEB rolls a 3, steals A from BEAUREGARD
3. BEAUREGARD rolls a 2, steals E from JESTER; die is given to NOTT
4. NOTT rolls a 5, steals D from FJORD
5. FJORD rolls a 4, steals H from YASHA
6. YASHA rolls either 1 or 5, steals C from CADUCEUS
7. CADUCEUS rolls 2, steals O from NOTT; die is given to THE BEE WITH MANY NAMES
8. THE BEE WITH MANY NAMES steals K from the alphabet; game ends
Once the players' stolen letters are identified, they can be read in clockwise order beginning at Fjord and ending at The Bee with Many Names as clued, spelling out the puzzle's answer, HEAD LOCK.
If you solved this puzzle and had a tricky time figuring out the seating chart even after identifying the campaign, just know that as someone who does not watch the show, I had just as much trouble. I was very surprised that there was no official media with a straightforward diagram of the seating chart (at least as far as I could find); there is this fan-made diagram showing the seating arrangements for CR campaigns 1 and 2, but I had to comb through a bit of campaign 2 footage to confirm that this image was correct, and I am not particularly good at telling faces apart. I do wish I had chosen a stronger puzzle mechanic than this contrived gameplay record, but I hope that any Critical Role fans solving this puzzle got to feel excited about that being the dataset that was used here.