Good news everyone!
I figured out that you can get the games running if you install the RPG Maker runtime package. I've linked to it in the first post and have added some screenshots. I also removed the small edits I made to get the game running (mentioned in the first post) so that these are totally accurate to what was released back in 2006. If you are in need of some Guyver content while the manga is on hiatus, well here ya go!
There's a message at the end of the Guyver 3 game which mentions that the games were made by Unito Guyva, who was a member on the old Guyver Board - I feel bad for not having remembered this as he was a good friend. He became inactive I guess 10 years ago or so (wow!) so I hope he's well wherever he is.