The Cambridge dictionary much more clearly specifies the romantic (and secretive) nature of a tryst:
ETA: I always got the feeling it implied the relationship to be short in duration, too, but I don't see that substantiated in any of the dictionaries. Hmmm.tryst
noun [ C ] UK /trɪst/ US /trɪst/ old use or humorous
a meeting between two people who are having a romantic relationship, especially a secret one.
Grey Wolf