Hey Maus!
I'm not exactly sure what's going on in the back end of your PC, but I'd double check install paths and such just to confirm. You also could try manually downloading the game and putting it in place yourself to see if there's something going on.
Alternatively, you could snag downloads from our Patreon. We have a few mirror options there. (You'll need a Patreon account but it's free to make if you don't have one already).
Also just as a heads up, any external site that hosts AHITR that's not directly uploaded or maintained by us, is of course unofficial and we can't assist with any bugs or save issues if they arise. This includes web browser versions. Saves are also not compatible either.
Hopefully you can pinpoint the issue with the space being taken up on your C drive though!