While you are correct that establishment's favorite seems more grammatical, in English it's not uncommon to create compound nouns by joining together two (or more) nouns:
and so on. Sometimes these are joined together (policeman) and sometimes kept separate (automobile dealership).
In general, you can assume the compound is whatever the final noun is, modified by the previous nouns. For example a "water distribution network" is a network (of pipes, pumps, valves, etc.) used to distribute water. In the same way the "establishment favorite" is the favored option of the established political party.
Again these kind of nouns are so common you probably don't even notice you're reading this on your computer screen while typing on your key-board while signals go back and forth over your network connection. You can even make up your own, once you get the hang of it.