"Appealing" in this sense most likely means "challenging in court" and it looks like his delaying a construction project has ended with him being sued.

This is not a sentence which anyone would say. Nor is it a sentence which anyone would write anywhere other than as a headline. It is an example of 'telegram-style' headline language in which several grammatical words are omitted, for the sake of brevity. The full version of this sentence is something like this: The activist who is appealing against the Miami Worldcenter plans has been told to pay $236K. Understanding English-language headline language is a real skill. When key grammatical words (especially auxiliary verbs) are omitted, it is sometimes hard to know what part of speech a word is. This is something which makes decoding the sense of the headline quite challenging, occasionally even for native English speakers.