Do other peoples besides centaurs use special or unique furniture that humans don't?
Yes! A lot of this depends on region too. For instance, in some regions people use chairs, and in others they prefer to sit on cushions or just the ground. In some regions people use eating utensils, and in others they use their hands to eat. So the following isn't true globally, just in some places.
All heavyweight species require heavyweight-rated furniture. Stuff like tables, chairs, bed frames, and so on are made of tougher materials to withstand the extra weight of these species. Of course these furniture pieces are much larger too.
Chairs made for ogres have a gap for their tails to poke through. More often, these chairs don't have a back at all, so they're more like stools.
Dishes and utensils are bigger and burlier to accommodate heavyweight species. These things have to survive the heavyweights' great strength and crushing jaws. Normal forks and spoons just bend like paperclips, and normal glass dishes break too easily. Heavyweights typically use dishes made of wood, metal, or stone.
Trolls have massive hands, so there are a variety of troll-specific objects like tools and dishes with fatter handles.
Heavyweights' objects in general are bigger. For example, a watering can meant for middleweight species might hold one or two gallons of water. But heavyweights are strong enough to hold much more, so their watering can would seem ridiculously large to a human.
Ogres and trolls don't typically use mattresses, and if they do, they're just hay or animal pelts spread on the floor. This is because their skin is so rough that they tear through fabrics quickly. If an ogre lays on your couch, I'm sorry to say your upholstery is not long for this world...
Minotaur dwellings have tall, keyhole-shaped doorways to accommodate large horns. (Fauns also have doors like this, but smaller)
Gnomes repurpose objects meant for larger species all the time. A spool of thread, for instance, might make a nice end table for a gnome. A child's dollhouse can even be converted into a real house in some cases!
Many gnomes find this tacky and don't wish to use hand-me-down trash from other species. Instead, they make their own furniture out of natural materials around them. They braid fur and hair of larger creatures into ropes or weave it into tapestries. Since they're so small, gnomes are capable of extremely fine detail work. No one makes finer jewelry or dollhouse furniture than they do. "Crafted by gnomes" is an attractive selling point for some objects.
Chairs meant for roshava have four arm rests instead of two.
Sirenes don't really use furniture underwater, but they do use it on the shore, and of course it must be made out of waterproof materials. You won't see sirenes sitting on cotton upholstery, which holds water and gets moldy. Instead, they prefer cushions and fabrics woven from water-repellent fibers like grasses and seaweed. This goes for cecaelia as well.
You'll never find stairs in a gorgon house because this species doesn't have legs. For the record, gorgons can climb stairs, but it's awkward and not exactly safe for them. Instead, they prefer smooth ramps and elevators. Wheelchair-accessible infrastructure doubles as gorgon-accessible!
Of course, all furniture meant for dworfs is shorter than it is for other species.
That's all I can think of at the moment!