Interestingly at about the 15:00 point of the vid he says regardless of whether he's flyin retractable or fixed he always does a GUMPS check.
Same here. This was drilled into me by my instructor from the first lesson. I almost only fly RGs, but when flying fixed gear I still do it. In fact, probably saved me from a gear-up not long ago (the usual scenario: distractions, high workload, etc). Caught it during the GUMPS.