Why do buses at some airports differ from conventional ones?
Apron buses are dedicated to transportation in the airport area, the one your show is located near the air museum at Salzburg airport / LOWS) in Austria. Similar buses are very commonly seen at airports:


Apron bus. Source.

The bus is traveling on short distances, it's maximum speed is 40 km/h, the price is lowered in proportion of the simplified design (more technical data).

Regarding the hidden wheels, considering the speed and the apron flat surface, this is possible for aesthetic reasons (many additional advantages come for free, e.g. fuel savings, protection against debris and stowaway). More importantly, the bus is a kneeling type type designed to accelerate passenger transfer. The floor can be lowered to:


To board and leave the bus more rapidly (no or small step).
To be accessible to everybody with no help, including when seated in a wheelchair (no lift required). 


Protecting the wheels also keeps clear the space needed to lower the bus, and prevent accidents. This may be of some particular interest in a region subject to important snow falls, like in Austria.

Wheel access is provided by a panel:


Aero ABus

But this type of buses also exist with some or all apparent wheels:


Source.

Airport buses may be wider than regular road buses, they are not subject to public road regulation:


Source.

The model shown in the question can carry 100+ passengers in standing position (5 seats).


Source.

Apron buses can also have a bridge included (see also mobile lounges):


Source.



Unrelated comment: Salzburg, in addition of being the birthplace of Mozart and a famous ski resort, got an airport well known for its difficult approach during winter snowstorms, with the aircraft flying close to the mountain sides.