DKDiveDude For what it's worth, I found a workaround for this. Unfortunately it meant buying another piece of equipment, but it was not expensive.
I bought a $24 HDMI switch off Amazon, one I've used before so I know it works. It's not anything complicated, just an off-brand 4-port dumb switch with a remote. I connected my laptop to the switch, and ran the switch output to the Roku TV. This completely eliminated the "game mode" on/off flipping.
I'm not a programmer, but I suspect the TCL is attempting to identify "gaming devices" by whether they output a 59hz or 60hz signal, the latter being more common to game devices. PCs however are more prone to wandering back and forth between 59 and 60hz due to power/cooling/CPU wait and other factors the system has to manage while also running games. This can cause screen tearing and other issues which gaming PC monitors deal with by using technologies such as Gsync, which are absent in most TVs. Clearly TCL's software solution to it is inadequate; I think the inconsistent frequency/framerate output is confusing this "smart" TV as to what kind of signal it is receiving. I could be wrong though, like I said I'm not an expert and this is just a guess.
The HDMI switch outputs a consistent 59hz signal no matter what is plugged into it, and isn't smart enough to inform the TV as to what devices are behind it, so the TV is happy to remain in standard non-gaming mode. And honestly a little 1-4ms input lag caused by this is MUCH preferable to the blinking and overlay obscuring my games.
Roku, please discuss this problem with your TCL partner. You've shot yourself in the foot with PC gamers as a result of this. I understand TCL is a budget brand, but it's better to simply not have a feature rather than have a feature that is so broken it makes the device unusable without additional equipment.