Learn Croatian: Radnici moraju čistiti hotel. - The workers must clean the hotel.

Because it follows a modal verb, which is the focus of this lesson. Just like in English, you conjugate the first verb (moraju - they must) and leave the second verb in its base infinitive form (čistiti - to clean).

The dictionary word for worker is radnik. Why does it end in a 'c' here (radnici)?

This is the plural form. When masculine nouns end in -k, that letter changes to -c before adding the plural ending -i. So, radnik (worker) becomes radnici (workers).

Since hotel is the object being cleaned, shouldn't its ending change?

Hotel is indeed the direct object (accusative case) here. However, for masculine nouns that represent non-living things, the accusative form looks exactly the same as the base dictionary form. If they were cleaning a person or an animal, the ending would change.