I would exclude Hopman Cup from the list in the title. It is a sanctioned ITF event as much as Davis Cup or Fed Cup, the mixed version, if you will.
I would say Abu Dhabi is an invitational tournament offering winner take all prize money.
It's similar to many invitational events of the past, which many of us saw in the 70's and 80's.
The question is do we limit General Messages to only ATP main tour events and the ITF majors, and ITF Davis Cup? Do we exclude ATP challenger events? Do we exclude other ITF events like Hopman Cup? Do we exclude invitational events like Abu Dhabi? What about IPTL? It's a legitimate tennis league with prize money, 1 million to the winning team, right?
If there are no ATP points and doesn't count on ATP H2H stats does automatically mean it is an exhibition? Not in this poster's opinion.
What should be the criteria to separate legitimate tennis competitions that can be mentioned in General Messages from exhibitions? Do we need the strict separation that the OP (formerly mod) suggests?
See Slasher1985's thread stating Hopman Cup is not an exho here