You could do it on Linux fairly easily with udev rules, but you’d need to write either a separate rule for every game or have each flash drive only contain a single game each with a generic executable name and path so the same rule works for whatever you insert.

Since most games are going to be built for windows you will also need the rule to invoke wine or steam (for proton). That part could get complicated if some of your games need specific versions of wine. Normally people handle this with Steam or Bottles, but both those programs generally assume each game you are launching has its own bespoke directory on your filesystem.