What you're describing is just basic video editing, jm. You take video from more than one source and you cut it together on the timeline. There's not really a shortcut or special tool for doing this since you ultimately need to decide which clips appear where.
Is there a specific part of that task you need with?
I was hoping to be able to edit and mark individual clips in a game and then save / mark each individual clip and use those in another project. I was able to edit a game and rename invidividual plays / highlights in the timeline and then if I rendered these, it would create the rendered clips as separate files. (which I could go manually rename).
I was hoping to be able to create a project per game and mark each of these to then use these to create invididual highlight videos per player.
I am somewhat new to Adobe Premiere Elements, so it is possible I am missing something or this is functionality that is only in the pro version.
This is certainly possible to do in Premiere Elements -- but I know of no editor that does this kind of thing automatically. You have to manually save each clip yourself, and then use a tool like the Elements Organizer to add metadata to make this highlight easily identifiable later.
It's a lot of work, but it's a pretty basic editing function.