Yes, you certainly can!
Join 50 other mobile speedrunners in the Mobile Speedrunning Discord: https://discord.gg/bpY8zeB
We have competitions, resources, new game suggestions, and tons of glitch discoveries every week. If you have a phone with a touch screen, you can join in!
totally wanted to write "yes, yes you can!" by reflex... nice clickbait :C
Hey @jocloud31, this is a complex question. It really depends on which game you play. For the most part, older devices will have some method for recording screen and audio. While I've seen a ton of people speedrun games on old devices successfully, some lag due to processing speeds can make it hard to pull off glitches and tricks. Thankfully, some leaderboards have switched over to In-Game Timer to make up for time loss due to lag.
There are definitely a lot of really credible speedgames on mobile now and the community is growing well. I've mentioned in a couple of other threads that mobile is the only platform that fits in with my real life commitments. If anyone needs suggestions then the discord is really useful.
One of the big draws for mobile over other handhelds is capture. Both the Samsung and iOS native recorder are now really good and there's a lot of free third party ones too.