Communities is more deeply integrated into the blockchain itself through the hivemind software. Hive-Engine is a 3rd party run system. So there is very little relationship innately.
If you want to distribute Hive Engine tokens to users of a community you would have to find a 3rd party solution. Hive Engine team have a system called SCOT that distributes tokens based on a voting reward model.
I am unfamiliar with other options of distributing tokens that is set up to automate.
But airdropping is an option... but airdropping to accounts is more of a manual process. It requires you having a list (which having a list of community subscribers likely accomplishes that) then running a transaction and signing for all those transfers of tokens.
Even PeakD has an airdrop system that even works for airdropping hive-engine tokens... but it is not a free and public system. But there are likely other airdropping software out there... but the rules for sending tokens would be up to you.
RE: How do Communities work?