I've tried to play this repeatedly, and the result keeps being that my laptop powers off. (I don't get a bluescreen - I just shut down.)

Is this happening to anyone else?

I play the game on a PC, not a laptop and so far I had no problem. It sounds a bit like you laptop shuts of due to overheating (at least I once had a similar problem with an old PC that was really dusted)....so maybe your laptop/CPU overheats and shuts down? Well, thats just a wild guess, sorry for not beeing able to help in a better way :-/

I'm playing on my laptop but I just started today. It hangs a bit when I first start the game but ultimately I've been able to play, I'm not through the first stage of the campaign though, almost that far. So far I didn't have any troubles. Might update your drivers if you haven't in a while might help.

To be honest, I would advise to look/ask in the Steam forum of this game. Like way too many other small Dev studious who sell their (EA) game via GoG the Devs of Spellcaster University ignore the GoG community and therefore the GoG forum is basically empty. I wish you best luck to find a solution, maybe on Steam instead of GoG :-/