I like it a lot, but one thing - I'm not so sure about the pretty bland drum loop you've got going for the whole song. I understand that something as slow as Swirls needs something like it to keep it moving because of the percussive nature of the piano (the synth in the original meant that the sound carried over, but a piano can't do this), but I'd like to hear a bit more "spice" than what you've got in the drum track. This would definitely take a bit more work, but perhaps if you added a simple repeating motif to the left hand part to keep the chords going; nothing to overpower the right hand, just a simple repeat.
Of course, since I'm lazy I'm not gonna suggest what that motif could be (and I don't really have the expertise to suggest something basic that would "work", being a violinist and not understanding what "goes into" playing the piano). :) Really great stuff. Sorry if it sounds like I'm focusing on the negatives here - really it's a pretty minor thing. :)