You have the potential to become highly skilled at TF2. I would say so more so that non INTP. TF2 requires logical thinking to win. Unlike most fps, your skill at aiming doesn't matter in TF2. What matters most is game sense, map control, logic, and of course teamwork. In call of Duty, (or even csgo), one person can win the game for the team, while in TF2, one person will never win by himself. Many times in TF2, it is the guy who does not fire a shot who is carrying the team.
When you learn all classes and maps you will be an unstoppable force. You will always know the most logical class to pick, or flank to take, or what action to perform, in order to win that specific situation. You will know what an enemy player is about to do just by looking at them, what they are holding, what direction they are facing etc. You will not be the guy dying the same way ten times by running into sentries, because you will be too busy with beautiful, game winning flanks and strategies to get rid of those obstacles so those dummies can run down the middle safely. Medic and pyro are both a great class for INTP.
In my 1000+ hours of tf2, id say 500 are medic. Medics require perfection when it comes to game sense and map control. After 100 hours, I was winning 90% of games and always top scoring. I just have to credit the intp here, I literally tuned out the real world for over a year. I lived entirely in a state of mind of mastering 100% of game mechanics, and learning every little thing before I quit. When I finally conquered tf2, I uninstalled it, and doubt I will ever play it again. On to the next thing.
My other favorite genre is turn based strategy, I find it very relaxing to not be rushed.
If you are good at thinking on a dime you can always try real time strategy, but you will be facing highly strategic players with 20years+ of experience.
TLDR: turn based, real time, puzzle, fps focused on map control, city builders, simulators.
Edit: sorry I forgot the most INTP friendly of them all: Kerbal Space Program is the only game an INTP ever needs to own. I swear I will be playing ksp when I am 75 years old. It is absolutely limitless when you add mods. You will never get bored or not have something to work on or start over on. I have 300 hours and have only explored earth and moon. I just made my first mars landing last week. I predict at 1000 hours I will be just getting my toes wet. My biggest tip if you get ksp, or any game for that matter, is to never ever watch a youtube video or tutorial of any kind. If you watch someone play it for you is the worst spoiler ever, but you wont realize it.