Is there a minimum separation between a landing aircraft and another crossing its runway?
When an aircraft has been given a clearance to land on a runway, that runway is exclusively reserved for the landing aircraft. (Except for LAHSO and "land after" operations, where only part of the runway is reserved for the landing aircraft).

That means that no other aircraft or vehicle should be on that runway. In this case, clearly something went unplanned. Either the crossing aircraft was not given permission to cross, the landing aircraft no clearance to land, or ATC mistakenly cleared both the landing aircraft and the crossing aircraft to access the runway. 

Pilots should always check if the runway they are accessing is safe, and in this case the crew of the landing aircraft did apparently observe the incursion and aborted their landing. The crew of the crossing aircraft noticed the landing aircraft a bit late, but you hear their engines spool up as well as they cross. The sound of the go-around thrust arrives second later due to the difference in distance. 

The crossing aircraft seems to be taxiing toward the rising sun so they may have been blinded and missed the fact that they were crossing a runway.