Some kids just dont like rides - and if he's ok with a ride that goes "round and round", I would think he wouldn't have vertigo, dizziness or nausea as those rides exacerbate the dizzy feeling.
It is very possible to have motion sensitivity around up and down but not be affected by spinning or motions on a level plane. I'm one of those folke who can spin like mad on tea cups, but get motion sick on even most kiddie coasters and ferris wheels. It started to develop around puberty and I've never outgrown it. I'm the only person I know who had to fight down not puking in
Disneyland's Radiator Springs Racers, and for most folks, the dips are just a mild thrill.
That being said, unless the child has pronounced allergies, I wouldn't push for them to see a doctor either. Most medications for motion sickness are also sedatives and can dull down and muffle the kids enjoyment of everything that day until the drug wears off. Is it really worth a 3 minute ride to ruin the rest of the day? And unless it's allergies, that's all they'll recommend. Been there, done that.
Please, don't force the kid and ruin Disney for them. Disney has some amazing shows, great character meet and greets, and can be fun just exploring for hidden Mickeys and playing the Sorcerer's challenge. Try asking the kid what they'd like to do and don't expect them to be like their twin. If they feel included and welcome to explore what they do and don't like, they may surprise you by asking to go onto a ride in the future that they avoided when younger, if only to see if they can handle it.
Trust me, even as an adult, I still find myself working up the nerve to try pushing my limits and seeing if I can do a ride I struggled with before. Every so often, I discover I can and it becomes my new favorite very quickly. Lucky for me, my husband thinks it's adorable to see me squealing with joy when it's a success, and buys me Dolewhips when it doesn't work out. He also never judges me if I'd rather pass on something. It does more for me to feel loved and supported, than it would ever feel if I felt pushed into riding a ride I wasn't comfortable with. And that in itself, is a a whole lot of Pixidust magic, all it's own.