My guess is that territorial fish have some sort of pheremone they speak to each other with. I also have a theory that fish from different continents sometimes send out mixed signals due to divergence of "languages". My honey gouramis treat the rest of the fish in the tank as scenery - they interact with eachother, sometimes some flirtacious chasing, sometimes territorial, but ignore other fish. The female apisto patrols the tank clearly with the attitude that she she owns it, yet ignores the cardinals and cories. She used to bully the gouramis, which was amusing as the oldest cardinals are bigger than her. She still tries to bully them - but they must have realised she is small and harmless - as they ignore her so obviously that it's obvious they are not ignoring her. They never try to bully her though.
I think gourami and cichlids are intelligent enough to adapt their behaviour based on their surroundings and tank-mates, but I would guess that when your gourami see the angel - they recognize it as a territorial fish with a brain, perhaps a really really malformed gourami, and the angel sees the gourami as weird looking angels, and since no-one wants sex, the angel then wants to to shoal with gourami and is maybe aggressive about it, the gourami responds to the proximity of what it smells as non-self territorial pheremones as "get out of my space". The angel maybe then decides to stand it's ground as it doesn't want to bee low on the shoal pecking order, cus, you know, breeding season might be soon.
This ofc is mostly conjecture - but it is my head canon as to why people say angels and gouramis separate tanks... they look and smell vaguely similar but do not understand each other.
