Dear Gurus Somewhere On The Internet...

This posting is related to a well known question about why rockets
turn eastward soon after launch.

Many answers to that question state something along the line of
"...objects on earths SURFACE move at a speed of...."

The question I wanted to ask is, what does this have to do with a
rocket that is not on the surface but somewhere up in the atmosphere?

Is the reason that earths atmosphere (meaning the gases in it) is also
in a constant movement eastward?

Or is there some other reason and in that case which?

Thanks in advance for enlightening me again:-)