Bidets like that either have a trap in the floor if through the floor, or above floor if connected from the wall.
They use an 1-1/4" tailpiece. Though the connection in the picture looks kind of odd for that.
The floor drain should have a trap too. If you see standing water in floor drain, that would be the seal. The water can dry out though if nobody washes the floor down. Take a cup and pour water in the floor drain to refill the seal there. That should keep the sewer gas out.
Of course, there's really no way of knowing if the plumbing is first world without doing more research on it.
My trips South of Mexico had some pretty funky plumbing. Guatemala had a lot of bidets like the one in your picture, and floor drains like that. India had floor drains too in the hotels.
India, notice the floor drain toward the back wall?
Here you have a handheld bidet wash near the toilet, very common, and a stand alone bidet.