Mounting a pull-up bar on drywall and metal studs?
My in-laws bought my son a pull-up bar last year and I found that, despite, their insistence on the box that we needed 16" studs, the fully assembled bar had holes 17" apart. With there being a major math problem there, I took to solving it by adding a 2x4 behind the top and bottom. I attached the bar with a 4" lag bolt on the top of both sides (to limit roll) and added 3" screws on the side I couldn't put their large lags into. It holds me up just fine. If you want to go the 2x4 route, I think it could work.

The bar you linked, however, has 6 lags on a track for lags (which is smarter). With 3 anchor points available for top and bottom, you shouldn't need 2x4s, unless you're worried about the top rolling and want to better anchor the 2x4s themselves (which shouldn't be necessary)

Your Option #2 won't work at all, because if it falls, it will roll off the top (the force is cantilevered so the top will come forward first), not fall straight down.