Is this Shimano Acera 8-speed cassette and chain compatible with a Shimano Deore 8-speed rear derailleur on my mountain bike?
Yes, the Acera 8-speed cassette that you link to should be compatible with an 8-speed Deore deailleur and shifters. The main compatibility issue is the spacing of sprockets, which changes with the number of sprockets and can vary between manufacturers. This cassette spacing cribsheet details the spacing for 8-speed Shimano cassettes, which should be the same for both Deore and Acera.
Edit: I should also mention that a cassette with a large maximum sprocket could be incompatible with some derailleurs, but this Acera cassette has a maximum sprocket size that is typical for a mountain bike.