I'm 8 hours from Greenwich, why is my sidereal time 10 minutes different from theirs?
I don't think the Google Search is passing any coordinates to the Heavens Above website to get the results the Search is displaying.
If you click through on the provided link in the search, Heavens Above gives the following default location:

Location:   Bristol
(51.4770°N, 2.5690°W)
Since Bristol is 2.57° West of the Greenwich Meridian, its Local Sidereal Time is about 10 minutes earlier than Greenwich.