This game will run on just about any PC.
Star Ocean 4: The Last Hope will be getting a re-release on the PS4 and PC via Steam, thanks to Square Enix launching the polarizing game in the long running series with an HD 4K remaster. The remaster’s release is actually not that far off- to be specific, it launches tomorrow (which I didn’t realize- it just crept up on us, I guess).
Anyway, ahead of this release of the remaster tomorrow, Square Enix shared a brand new trailer for the game, showcasing some of the story sequences in the title. They also went ahead and shared the requirements for the PC version of the game- I think your mother’s old laptop should be able to run the game, honestly.
Of course, it won’t probably run it in 4K- the PC version of the game will support 4K, but I imagine you will need a reasonably decent rig for that. You can also play through the game in 4K on a PS4 Pro; the PS4 itself will run the game in 1080p.