Personally I don't think companies can do a great deal about remakes. If you used their media and title then they do have a leg to stand on. But you can have the same conversation about Doom/ Duke Nukem / Unreal / Halflife etc etc all basically the same game. Or indeed any sideways shooter where you're a little spaceship. Many could argue that game x is a remake of game y because it about a space ship shooting lots of bad guys.
Really I think you've got 3 kinds of remake.
Retro Remake : Use the same media, maps and title no-profit
Retro Remake + : Use the title and maps but update the sound and graphics, no-profit.
Remake : Take the general gist of the game and throw your own spin on it not using anything from the original except the idea.
I think the first 2 you could potentially run into legal problems if the original authors so wished.
I think with the 3rd your perfectly in your rights to claim the original game as inspiration, much like doom was for unreal.
Really I think you've got 3 kinds of remake.
Retro Remake : Use the same media, maps and title no-profit
Retro Remake + : Use the title and maps but update the sound and graphics, no-profit.
Remake : Take the general gist of the game and throw your own spin on it not using anything from the original except the idea.
I think the first 2 you could potentially run into legal problems if the original authors so wished.
I think with the 3rd your perfectly in your rights to claim the original game as inspiration, much like doom was for unreal.