I have been speedrunning games for about a year now, but for my own sake. I would do it not timing myself or posting any of the times to any leaderboard since my PC in the past hasn't been good enough to record or play most games. Now I have a close to the high-end computer and can play just about anything. I've started to now get into competitive speedrunning and have has issues on some games that might be worth it to speedrun. I'm into just about anything and of course, I know most will already suggest platformers and I have been thinking about getting Celeste. Money isn't really an issue but I do like the fact of speedrunning free games. (If you were to look at my account I've been doing The Very Organized Thief) Of course, I am willing to put the time into something. I just wanna know some games you guys play that are fun to do and you feel like you're actually making progress in the run.
I'm going to suggest platformers just because this is my favorite type of games (along with puzzle, metroidvania or precision-platformer genres). If you want to run free games, you can search web games in the games list - everything will be free. There are also free PC games in sites like Steam or Itch.io, most of them will have the PC platform so it will be harder to search specifically for those.
You can look at my profile to see if there is anything to your liking, I mostly run platformer web games from several kinds, mostly up to 20 minutes.
(Although it can be funny to think that a high-end computer is used to record web games)
Edit: your YouTube link does not work.
This kind of thread tends to make people answer about the game they already like and run, which most probably won't be the games YOU want to speedrun.
If you want a popular game that most people care about, play Super Mario 64, Super Metroid, The Legend of Zelda: Ocarina of Time, Dark Souls, Sekiro, Bloodborne, Super Mario Bros, Celeste, Resident Evil 2 Remake or 3 Remake... These are some titles that the majority of runners like.
But, for something more specific, it's important to know what kinds of games you like more. Like, FPS, Platformers, RPGs, Puzzle Games, Fighting Games?
My advice is just go onto a game website and choose a game. If it's fun to play casually, try speedrunning it. It's that simple. I do that sometimes when I'm bored. Some good sites:
https://www.lexaloffle.com/pico-8.php Lexaloffle is a site that hosts all pico-8 games. There fun stuff like platformers, puzzles, and rpgs. This is the software celeste classic was made in, as well as many other games. https://www.bontegames.com/ Bart Bonte is a really talented game dev who made some of my favorite puzzle games. He runs a blog where he not ony posts his new games, but also shouts out other puzzle games he has played. If you like pzzles, this is the best website to go to. https://www.coolmathgames.com/ I don't think I need to explain this one. Coolmath has almost every webgame ever made. seriously. Their selection is huge.
Catastrophe Crow and Boodunnit?! are really good. Boodunnit is on itch, gamejolt and steam for free. It's a chibi cute 3D platformer where you solve your own murder. And Catastrophe Crow is a horror N64 3D platformer game based off of an ARG, no you don't need an emulator the download link is on the speedrun.com page
Boodunnit?! : https://www.speedrun.com/boodunnit/ Catastrophe Crow : https://www.speedrun.com/crow64