I am in the same boat as you, and my laptop is from 2010 and unfortunately only OpenGL 2.1 (so for example it can't run Battle Brothers). I also tend to avoid Unity games for this purpose.
What type of games are you searching for (crpg, rts, space sim, survival .. etc.)?
Also you know that Steam has an offline mode, so that you can download and install the game online, and then run it in offline mode.
Yes, I'm aware of Steam's offline mode, but the laptop is so old and cranky that if I went online and loaded up steam it would probably collapse under the weight of so much on-line activity. It simply can't can't cope with being on-line in the first place. Even going onto Big Fish to buy and download the next Nancy Drew game is an exercise in extreme patience.
Just downloading the game onto a stick and then putting the stick in it is such a massive QoL feature that it's my massively preferred option.
Not to worry on recommendations, I suddenly remembered @xSamhainx; talking about the enduring quality of Majesty (2000) and also remembered I had watched a respectable Youtuber give it a 5* recommendation a few months back, so that's my next new adventure.
I also remembered Dorateen has released his Knights of the Chalice 2 Mod Harkenwold on Nexus Mods, so I've downloaded that as well. These two should keep me busy for a while.
If you're looking for some good recommends from me, then some of the games I've played for the first time like this over the past few years have been, in no particular order:
Tales of Maj'Eyal - Roguelike, 3.25/5
Stronghold HD - mission-based RTS 5/5
Avadon 1-3 - Vogel RPGs 3.75/5
Eschalon Books 1-3 - Indy RPGs 4.25/5
Legend of Heroes: Trails in the Sky 1-2 - jRPGs first 4.25/5, second 3.5/5
Anno 1602 and 1404 - Naval and builder RTSes first 4/5, second 3.5/5
Legends of Eisenwald - Indy strategy RPG 3.5/5
Tropico 1-2 - Economic & Builder RTSes, both 3.75/5
Banished - builder RTS 3.5/5
Might & Magic 1-2 - extremely old blobber RPGs, 3/5
Caesar 2-3 - builder RTSes first 3.75/5, second 3/5
Zeus + Poseidon - as Caesar, 3/5
King of Dragon Pass - TBS 2.75/5
Port Royale - Naval & Builder RTS 4/5
Nox - aRPG 4/5
Geneforge 1 - Vogel RPG, 3.5/5
Avernum 1-5 - Vogel RPGs 5/5
Age of Wonders 2 - fantasy TBS 4/5
Age of Wonders 2 Shadow Magic - as above but 5/5
Crusader Kings 1 - Paradox RTS 3.5/5
Paper Sorcerer - Indy small blobber RPG 3.75/5
Edit: oh yeah, and tons of Nancy Drew games and also Hidden Object games from Big Fish Games