No I think it's 3-4' down so most stakes should be fine. I have almost exactly the same one as what you listed here except it's green. I like it ok except for the zippers on the doors, my mom has one that's a little bigger and older and the plastic zippers wore out this year. Dad has old t-posts in the shed, they are more like 6 or 7 ft but still might work ok. I think they went with wood stakes on theirs, and so far theirs has survived although I know they've worried a few times.
This spring I was considering removing the plastic cover and just having the shade cloth up so that it was a shade house for my hoyas and such. The GH just gets too hot in the summer. I did this before with one I had when I was back in B/CS, and it worked well for them. I'm just a little skiddish about doing it right now given it's not even the middle of March.