https://www.youtube.com/watch?v=9V-A3SDZlR0
In the hostel at Shprinzak 99, they have a water dispenser in which its pump have the same horrible noise of a pump of a coffee maker.
What causing this?

Because it just likely uses the same style pump.
It would make sense, if it has to pass the water through some denser filters, which pose considerable backpressure.

But in other water dispensers like TAMI 4, I don't hearing this noise.

First does the "other" dispenser has the same functions (mainly the filtration, need for sufficient inlet pressure vs ability to operate when the water pressure gets low...)?

And seconds I do not see that much strange when different manufacturers use their own different solutions.
Plus there are very big differences among how these pumps behave (mainly the noise,...) among various manufacturers and also depending on the way how exactly they are installed in the machine (how much of the vibration gets transmitted towards the machine body - even in coffee machines, the noise these pumps create varies from loud rattle to completely inaudible, while operating the same pressure). So I see no surprise some cheaper model creates more noise than some more expensive, better refined one.