I'd just play quick arcade-styled games if I knew I only had 1 or 2 hours a day. I wouldn't try to commit to a long-lasting single-player experience only to eventually finish it two years later (if I did that I would only try it during vacation).
Instead I'd play Beat em' Ups (8-bit and 16-bit era ones) like Streets of Rage 2. I'd play arcade styled, light-hearted non-commitment racing games like Mario Kart or Sonic All Stars. I'd play Shoot 'em Ups (side scrolling or top view ones) in the veins of R-Type, Ikaruga, Raiden, Thunder Force, Gradius, etc. I'd probably give a few rounds and matches to Fighting Games (Street Fighter series most likely, since I find the gameplay of most of its games to be pretty friendly for most characters; especially the SF2 series, SF2 Hyper Fighting and Turbo, or Alpha 2 as well).
When it comes to FPS games, there's plenty of games that have short maps and don't required much thinking or 'research' (exploration) on your part and have zero long-lasting RPG elements in them (saving a lot of time from potential grinding) such as the DOOM series (not DOOM 2016, but the original ones up to DOOM 64, if you do play them then get yourself the GZDOOM engine which can run all the DOOM engine games including Hexen, including famous mods like Brutal DOOM; which in my opinion is the quintessential Magnum Opus of the franchise). In more recent years there was Painkiller, also Hard Reset is a very solid retro-styled FPS with more modern graphics, and on Steam there's a bunch of other remasters of old(er) FPSes like the excellent Turok 1 and 2 remasters for example, or the Steam (or GoG) versions of Duke Nukem 3D as well would fit that bill.
If not, there's decent puzzle-styled games that can be fun to burn some minutes here and there like World of Goo (superb soundtrack by the way; have to mention that), or one of my favorites if it comes to just burning time on a rainy day while not feeling like playing anything else would be Bejeweled 3 (I got it on Origins, not sure if it's available on other platforms) and Peggle. And Plant Vs Zombies (the first one) still holds pretty well for that kind of quickly-played game.
I've been in your situation from time to time a few years ago. That's what I did and it was just fine. I had about 2 hours (max) when I got back home for myself once everything was done. I'm not a "TV person" much so I still sat down in front of my monitor instead and went on YouTube, checked for some documentaries to burn time and when I had about 20 or 30 mins left before going to bed I'd play the types of games I've mentioned here. So to reiterate... that would be Arcade styled, light-hearted games, or games that don't require commitment in any way possible; I only made sure that all the games I played had a "save anywhere anytime" saving system; otherwise I'd just avoid them, no time to worry about dying or failing a mission or a challenge before a specific period of time, or a checkpoint somewhere.