Thats a hard question for a number of reasons while both are pc hardware you have alot of things to consider
Specs of the machine and requirements of the game
Type of game, (some games are 64 bit, some are 32 bit)
Windows version and requirements.
with all that being said, being that these are games made in 2017 onwards, i would say on a stock or nikos muti style harddrive image you would have a Absolute Zero chance of them running.
beacuse, they are likely going to either require, newer Dependencies and Maybe even be 64 bit applications that simply wont run
Now in a hypothetical world where you replaced the os on the ttx2 to say windows 7x64 and managed to find drivers to make everything work, well id up the chance of suesss form Zero to 100% chance of it booting, however, booting docent mean playable framerate id say your looking at a 10-30% chance anything runs well there.
Now if you took the extreme approach of doing all the above, installing 4gb of ram, installing say a newer Gefroce gpu such as the 660 Ti and upgrade the CPU, to the core2Extreme
then yes a game in thoery should play and run prefectly fine,
but the real question at that point is why?
You would have a much easier time, rather then upgrading old hardware, and finding specfic driver versions ect to just buying a new gaming pc, slapping your fio card in it, then everything would work
as you stated your only goal is to play it on a cab, well theres a million ways you can plug normal pcs into cabs. even if you dont want to use the real io boards.