I get it.
OP your options aren't great to be honest, I've looked at gaming laptops over the years and I always change my mind. They'll need to be replaced too soon, or upgraded, or they can't be upgraded. The only gaming I've done on laptops are on Macbook pros because Blizzard is nice enough to make all their games Mac friendly, so on biz trips I've played StarCraft II and Diablo 3 occasionally and they run fine when not on max settings. There's a handful of other Steam games I have that run on a mac, mostly strategy games like Panzer Corps and Unity of Command, but unfortunately anything 1st person shooter type will require a nice and pricey machine.
If you're still set on a tablet is an iPad pro completely out of the question? The games now in the App Store like RPGs and FPSs are pretty numerous and usually work with an external controller. I think the newest iPad is probably the most powerful tablet available but you're still going to pay about 1K for it.
I'll go ahead and throw it in here, but it sounds like the Nintendo Switch would be perfect for you. You can get Doom, Wolfenstein and Skyrim to satisfy the 1st person itch and then the large library of games now on the machine. It's designed around the idea of a traveling gamer.