The Berne books Rao cites as explanations of Gametalk are solidly good entries in of themselves, although it's probably best to use an LLM to get search results of the best introductions to TA first to see if they've been surpassed.
Here's one question I asked:
"How does Eric Berne's Gametalk as interpreted by Venkatesh Rao signal to the sociopaths that those who engage in them are losers worth talking to? Distinguish between "channels" that Eric has identified as well as new signals that Rao or others have discovered."
Mike is the archetypal nihilist (Sociopath or Loser), the other two would potentially be engaging in a Clueless interaction if Mike wasn't there, according to the Scott/Rao theory of jokes, you need 3 for a Loser joke.
The preceding banter seems to be more of a Loser Gametalk: no social status is at stake; it's irrelevant to their white-collar role. Mike's Straighttalk intervention is typical of a sociopath; the wall breaking joke is that these Losers don't know what his real job is. If they did, the pointless but playful debate would have died a violent death-- because it'd get too real
If these were Clueless middle managers debating their value to their company, it might even be out of character for Mike to notice them..