While it does get pointed out, they enter the saloon to the sounds of Oingo Boingo's "Weird Science" on the piano. It's hard not to see this as a poke at Westworld (2016), which plays a lot of modern music on its saloon organ.
Jennifer makes one subtle reference to the classic Oregon Trail game as soon as Mr. Cole suggests going back to 1852 to retrieve whatever weapon the Seers/Primaries hid away to fix the endless time loops.