Civ VI was in part a sop to the Civ IV players who didn't like Civ V, and it seems they were deliberate in revisiting some of Civ IV's civs over adding new ones (though Jayarvarman is new - Suryavarman II was the Civ IV leader). As for the Khmer, they were the most obvious representative for SE Asia when Civ first included that area as being both significant and well-known to Western audiences. If you're going to include one civ from Southeast Asia the Khmer are the best option on historical as well as popular recognition grounds. Jayarvarman VII also qualifies as a 'big personality' - he pioneered the major phase of Khmer expansion, defeated the Champa who until then had been their major rivals, and stuck his face all over the Bayon.
I don't think it was until Civ V that Firaxis really paid attention to the non-Western part of its audience in terms of civ selection, and Burma is much more poorly-known in the West than it deserves to be. That we had to wait until Civ IV to get Southeast Asian representation at all, and until Civ V to get Indonesia, speaks volumes (especially as even when they added Indonesia they used a modern name despite the civ being effectively Majapahit - and unlike Civ VI, Civ V had the Majapahit capital in its city list).
If the Khmer aren't back for Civ VII Burma's a reasonable prospect - Siam rather backfired as it was one of the civs Firaxis said they added for local appeal, and controversy over the leader image actually ended up with the game being censored there.
I don't think the Philippines is an especially good option, since Southeast Asia is especially rich in developed urban societies on both the mainland and Indonesia but not in the Philippines - for a comparatively small area it would be overrepresented with as many as three civs, and so the Philippines would be ousting a more appropriate civ.