I guess this goes for a lot of different scenarios:
1.) A game gets "remastered" for modern PCs, or at the very lease got a GoG re-release.
2.) A game comes out on one platform (console/PC) first and then you re-buy it for the other (GTA5, Diablo3)
3.) You had the game on physical media and lost/broke it and re-purchased, either digitally or physically (again).
OK I guess this goes for a couple different scenarios.
I bought Diablo 3 twice. One for PC, once for Xbox One. To me, they feel like completely different games thanks to the input methods and gameplay choices made to accommodate them. The PC version is a precision-laced dungeon crawl, and the console version is almost aRPG like - Zelda probably isn't the best example, but if you played Record of Lodoss War on Dreamcast (another addictive action-RPG) or Beyond Oasis on Genesis...it took me back, I'll tell you that much. I liked the demo quite a bit on PS3 but the lower monster density made for kind of a dull experience, and I knew the Xbox One version would be perfect. So I bought the full PC game + expansion, and then last August at release I bought the Xbox One version. And to me it was worthwhile, because it really does feel that different. Separate, but related.
Loads of games have come out on PC "twice" and on a couple occasions I've bought them, and I've had to replace my StarCraft/Brood War and Diablo II/LOD discs. I think I've bought those games like 3 times each.
My question to you is, have you ever bought a game twice? Was it worthwhile? What do you require to do it?