Swinging is one of the best mechanics in the history of games, it's always fun.
I love the cat. The music is great too, I'd come up with an excuse to add more songs, for example have a different song on each level and they progressively get more intense.
My only objection is that the solid objects make it hard to judge how far they are when grappling, maybe you could give them some texture. It can still be something minimalist like the grid in Tron, for example.