I definitely like what I see so far. I would like to see some mobility work, moving over corners while wall climbing doesn't work very well, if at all, and falling is quiet easy. A nice fix for the fall would be automatically deploying a strand of web to catch yourself so you can crawl back up or all the way down. I would also like to move a little faster or at least have the option to.
Solid start, looks great. Do you have any gameplay in mind?