I have a Lumia 920 and have also experienced lag on a lot of games, even before 8.1 There are two parts to the problem (possibly combo of both or separate issues on their own):
1. If Gameloft actually optimized their code for the higher end 60hz refresh rate screens and our chipsets for smooth performance, as opposed to just copying the code over and simply porting it to Windows Phone, there would be smoother performance. They've pretty much copied apps over and told us "you're welcome" without caring about performance.
2. Doubt this makes much of a difference, but we are still missing drivers that the Cyan update will bring. These could include all kinds of behind-the-scene changes and (seemingly) unrelated stuff that may enhance graphics performance in games and throughout the OS as a whole as well.
I'm a little less hopeful in #2 solving a lot of the problems (when it comes to the games performance, not the OS) and have come to the conclussion that, until Gameloft views Windows Phone users as valuable as iOS/Android users (as this is even a problem on Android as well with fragmentation with the huge array of chipsets and devices), we won't see any improvements in the quality of games....