Leaning more towards NTA but you're far too angry - as stated, he has his own playstation and should be using his instead of yours full stop.

However, you don't mind that he uses yours on one specific condition which he has broken. I understand the frustration of losing a games progress, I know I would be furious if I lost some of mine but you're lucky it was with a short game and not anything else.

He is still a kid and it could have been an honest accident and he could have possibly been too scared to tell you or didn't realize. How exactly did he react when you confronted him about it with your mum aside? If he seems genuinely sad and apologetic for it then you should be able to look past it and tell him he should use his own from now on or give him another chance.

If he genuinely didn't realize then help him understand.

If he denied it and didn't want to take any responsibility then it is understandable that you're a bit more angry - if that's the case then get over it and refuse access to your PS from now on.