This.
If a baby (or adult with a migraine etc) was sleeping you would ask kids to leave them be. Their cousin asking for quiet time is just asking for that and, in fact, showing self awareness of how and when they need time to self regulate. If they are upset by others playing by the pool then either they or the noisy people can move - hardly the end of the world.
Discussing school - think of it like avoiding politics or religion around a family member that disagrees with you vehemently. Surely you would try to do that to keep the peace? Just ask your kids to be sensitive. If they are 11 or so, they are old enought to be sensitive and, let's be honest, probably already know that their cousin has problems with school. A steer to ask them to avoid discussion of school around him will avoid any well meaning (or mean!) questions about how school is going. They will be on holiday, so probably not even wanting to think about schol, and sound old enough to have plenty of other things to talk about.
Competitive games. I hate it myself and feel uncomfortable playing competitive games that get too emotional with gloaters and bragging winners. I hate monopoly. But a game played collaboratively, or where players "compete" but are supportive and friendly with each other is fine for me. So, they want to throw dive sticks into the pool? Then they are a team and can all have an ice cream once they have each, in turn, retrieved the sticks x times / from a certain depth, etc. Ask DSis what might work and, if necessary, buy some collaborative games to take before you leave. You just need to be flexible.
Finally, eating outside. If one of your kids had an allergy to pollen or bee stings, so that suffering or fear would make eating inside more comfortable, would you be understanding and plan some/most meals to be inside, or would you give them their plate inside, sit outside with the rest of the family, and laugh at them through the window? I mean, you can still eat outside (informal meals, snacks, any meal not for the whole group), you can enjoy a drink on the patio as the sun sets, you are just being understanding of your nephew's needs. Kids may prefer to eat as a group inside anyway, with an adult meal outside, at least some of the time.
I agree some of this may be unnecessary. Only time will tell. But your DSis has probably had an awful time trying to help their son. School avoidance sounds tame, but is often emotionally wrenching - seeing your child distraught, and not knowing why or being able to help them, whilst the school and society tell you it is because you are a bad parent. She may be near rock bottom herself. Having the diagnosis, and feeling like they are finally able to help their (often) distraught child must be such a relief. Your DSis is telling you what would help her, your nephew, and everyone else to have a fun and relaxing holiday. Surely you love them? Surely you can work with them in these (relatively) small ways to help everyone have the relaxing break they need? Speak to her. Understand what might help and what is possible.