How does spectroscopy determine what depth of the remote atmosphere a particular gas is at? This article mentions "...there is less methane than expected in the upper atmosphere" of an exoplanet. 
How does spectroscopy determine what depth of the atmosphere a particular gas is at? Is it a matter of evaluating the pressure at which the gas would emit/absorb a given wavelength?
 A: In this case it is probably that only the upper atmosphere is excited enough to emit and only light from the upper atmopshere will be able to reach us without being absorbed
A: There's a review article describing the measurements on the Arxiv. At wavelengths where you'd expect methane to be absorbing more energy is observed than expected. That suggests there is less absorption by methane and hence less methane than expected.
The data has to be interpreted by fitting it to a model, and it's the fits that suggest there is less methane than expected. I can't see anywhere in the paper where the authors specifically say they're only considering the upper atmosphere. However the models include cloud structure and presumably it's a feature of the models that the upper surface of the clouds dominates.
I should add a disclaimer that my expertise in these areas is restricted to being able to read (the paper) so read the paper yourself rather than taking my word for it :-)
Re your last question, in principle you can tell the pressure of a gas because pressure broadens the spectral lines. The broadening from gas at high pressure (and therefore presumably low height) can be seen because the broadened wings aren't strongly scatter by gas at greater height. There is some discussion of this in this paper. Note that the exoplanet observations are far too low resolution to see this effect.
