Might as well give an interim update.. Seeing as how nobody on this forum had advice to offer, I went ahead and put in a request for service via my Tesla phone app on 29Oct. That turned into a mobile service appointment for 8Nov, but in parallel, someone behind the service app curtain sent my car an OTA update (or claimed they did), and asked me to install it. Didn't help, but remote efforts were ongoing and the in-person mobile servicing got pused to 14Nov. That was followed by a couple more software updates, and a factory reset that the remote tech managed to do a save/restore of my relevant personal state for. The games still wouldn't start, though.
This morning (11Nov), finally, I got another message via the service function of my phone's Tesla app. Hopefully, they won't mind me quoting it here:
"Good morning after reviewing some more documents and information we have found this to be a known software issue at this time. The games manager is missing the security signatures to be able to load. This is actively being investigated by our engineering team at this time and a fix will be anticipated in a future firmware issue. No further diagnostics are needed at this time and hardware replacement will not resolve issue"
I'm grateful to have an explanation of the problem and assurance that it will be solved when the next free elections are held, but there are some irksome things about the situation. If it's a known issue, why did it take the better part of a month for whoever put in a couple days' labor on the issue to discover that it even existed? Doesn't Tesla maintain an internal searchable knowledge base for this stuff? Are ALL the games installed as a single module (else why wouldn't it be possible to replace them individually)? Also, to judge by the interactions I had with whoever was holding up Tesla's end of the service message conversation ("We tried another install. Tell us if it worked!"), Tesla could really use some more tools that would let them execute commands remotely. There are probably more things to whinge about, but I'll stop with wondering why, if the issue really IS a "missing security signature" on one of the car's supposedly built-in features, didn't the detection of that error get logged?