Papers Please played pretty well on iPad, haven't tried much else tbh. I played through Max Payne on an android tablet once, it was rough, same goes for GTA:SA.
I think there's openTTD (transport tycoon) for all platforms? At least it used to be available on iPad as well, pretty sure it's on Android, and it's free on Steam. Runs on anything made past 1994.
Wish I could find my old copy of RollerCoaster Tycoon, also runs on anything and drowning your guests in creative ways never gets old.
OpenCnC/OpenRA also exists and can possibly run on weaker machines if you are looking for some classic RTS gameplay.
Or there's always ZDoom for example with BrutalDoom mod, if you are more inclined to play something fast paced. It should run fairly well (works fine on my old 4th gen i5 laptop, no gpu)
SimCity 4. It's still a great time waster and should run on potato, it's among the couple of games I always keep installed on my craptops.
Beyond All Reason might run on a mediocre PC, not sure as it is fully 3D. It's a free successor to Total Annihilation.
For native mobile games, for years I used to play a car racing TCG called TopDrives. It was pretty good on the free-to-play side, watching ads was fully optional, loads of free solo content with meaningful progression, don't know how bad it got since I stopped. Just don't get addicted.
For purely web based, you could check out the
flash games archive and there's a similar site for old DOS games where you can play in the browser, although I can't find it at the moment.