When an intransitive verb has a preposition prefix, it may be treated like transitive verb, one that takes the same object as the preposition. This is most useful to make passives or to coordinate verbs.
Ŝi eksciis kaj pripensis tiun fakton. La loko alvenita...
When the verb occurs by itself, it's common to keep the preposition.
Pripensu pri tiu fakto.
One could argue that "aliĝi la klubon" is OK by the preposition-substitution rule, but "aliĝi al la klubo" is what you will hear most Esperanto speakers say.
Edit: it was brought to my attention by one of the course authors that "aliĝi la klubon" used to be a sentence in the course, but has been removed as an error. See this thread.