Is 1 hour 20 min enough time to make a connecting Hainan Airlines flight with only carry on luggage?

May I know which transfer you will take? International to International or domestic to international? Anyway, generally 1.5-2h is needed for a transfer. So your time may be tight.

And if you use Hainan Airline for the whole trip and the airline arrange the timing. Hurry up and probably you can catch that.