My BabyGirl is demanding but she is not hyper. She demands to be petted and massaged constantly from my husband and I and will alternate walking back and forth between us. Makes it hard to get anything done on my computer but I can't resist her cuteness. Unfortunately she doesn't do any ball retrieving or toy play. She just chews her antlers when she's had her fill of our attention. She gets a 45-60 minute leisurely walk every night and she sleeps well after that. Maybe Rex just needs a good walk. Just make sure to walk him in the early evening when it is cool cause bullies can't take the heat and provide plenty of cool water when you get home.
I got the quintessential lazy bulldog. She's got a routine (she came up with it, I didn't!) - she wakes up everyday at around 7AM, I take her out to potty, then we play for 30 minutes (she's really hyper when she plays - like full-on energy, running full out - and man, she's fast!), then she eats, and she naps. Wakes up around noon, walks around, drinks water, asks for rubbings/treats, then she naps again until my husband comes home from work. Eats her dinner, then we go walking for an hour, then she's done for the day. She's such a slug. LOL! We try to take her out to the park as much as we can to get her more active.
But then, she's a 3-year-old bully, so I'm fairly certain the laziness comes with age.
Our boy was very hyper as a puppy - would never stay still for long enough to take a photo, so nearly all his puppy shots are blurry! He also had some of the "terrible twos" but after that settled down a lot, and now at five our walks are pretty leisurely, although he still does get into an excitable frame of mind now and again (rarely has the zoomies now though - miss those a bit!)
I think it does depend on the dog.
OP - you seem to be worried about the demandingness/whining. You simply need to ignore the behavior - look away and don't react. After a while it will lessen or even stop.