To explain, I had to downgrade my computer from a gaming laptop to something lower end, due to my gaming laptop breaking. My gaming laptop was of course able to link games to my Quest 2 and I could play them like that. Unfortunately, my new computer is having the "graphics card not compatible" issue. Is there any way to play the games that I purchased on the Oculus app on my Oculus device without streaming, or am I stuck?
It depends on the games.
If a game is on this list: https://vrdb.app/rift/index_us.html?filter=Cross-Buy+Apps
then it is cross buy. That means when you get the PC version (only from Oculus, not from Steam or Epic), you also get a free Quest native version that runs without the PC.
These won't show up automatically in your Quest 2. You need to go to the Quest 2 games store and look for each game one by one. The price will be listed as Free if it's cross buy. Buy it again as free to get the Quest 2 version.
Otherwise, Having a good enough PC is needed to do PCVR on a Quest 2. I've heard of some people trying cloud gaming services (nvidia has one I think) but I don't know much about how successful that is (not something I'd want, lag would be horrible from here in Australia).