Sounds to me like they had a lap child and an empty seat next to them, but Delta wouldn't let them place the lap child in the seat because they overbooked the flight and wanted to give the seat to someone else. I think I'd feel the same way if I were the parents, but the 18 year old never checked in so Delta already allowed someone else to take his spot and it wouldn't be fair to the person who got the spot. So I'd be irked but I'd get it and let it go.
This incident had nothing to do with the guy being Asian. Broad statements like these hurt the cause of addressing real discrimination.