A few ways come to mind.

As regards passengers:

- Encourage passengers of all sexual orientations to give them business;
- Actively and publicly promote transportation to gay-and-lesbian-themed events and venues;
- Ensure that customers know that they are welcome on board, regardless of their sexual orientation.

As regards employees:

- Extend benefits to same-sex partners;
- Prohibit discrimination based on sexual orientation or gender identity;
- Promote acceptance of all sexualities throughout the organisation.

There are many airlines which tick none of the above boxes. I would say these are "not gay-friendly".

They're not claiming to be a "gay" airline (which would IMHO be rather silly), they're claiming to be a "gay-friendly" airline. There is a very clear distinction between the two, and in my mind it makes perfect sense.