I really liked the design and thought it was generally a lot of fun. This was really clever, especially for your first game.
The only tricky part was clicking on things to grapple on to while in midair due to the camera movement. Maybe a more generous length or some kind of lock would help that. I do like the momentum based physics though.
I got stuck at the part where you had to grapple multiple times in the air.
EDIT: From reading the other comments, it seems the game DOES have audio. For whatever reason, it won't play in Safari. I'll try in a few other browsers.
Again, great job!