..:: PCSX2 Forums ::..

When I check the compatibility page, I see that specific version of PCSX2 is specified for each game. I know that this is the best version to run the game on. But will the game run on newer version of PCSX2?

In most cases yes. Normally compatibility decreases.

This is in contrast to speed. Often the older versions have less requirements than new ones at default settings.
But in newer versions you can also have new speedhacks (for example skipdraw if you are gpu-limited)