Debian install of what? I thought we were talking about player firmware (Radio or Touch).
I guess you mean either LMS or desktop Squeezeplay.
For Squeezeplay the git revision is in the package filename: squeezeplay_7.8.0~22901ff_all.deb.
For LMS the revision used, in both the filename and as reported via the WebUI, etc., is the Unix timestamp of the revision: logitechmediaserver_7.8.0~133664662_all.deb. It is not trivial to correlate this with the git revision-id but it should also not be that difficult.
Well, I seem to be doing something wrong as I always get "Thu Mar 28 02:04:22 1974" as a result when using the current LMS build 133664662 's Unix timestamp ?