Translation:Ten thousand and sixteen guests sleep in this hotel.
Tíz itself is spelled with a long "í". Since it's unchanged in the compound word tízezer, "í" remains long there. But in certain forms the "í" is shortened, and tizen- is one of these forms.
Note that this added "-en" is not the -n suffix. If you add that suffix to tíz, the "í" stays long: tízen (So "tizenhat" -- "sixteen" with a short vowel, while "tízen felül" -- "above ten" with a long vowel)