All state machines are used to parse. Parsing doesn't have to be "parse text from a text file". For instance, a TCP/IP stack uses a state machine as well. It's "parsing" the network packets, and it's using the content of the headers, combined with the current state, to determine what its next state (if different from the current) will be.
In a broader sense, state machines (which can or cannot have memory - FAs don't have memory, PDAs and TMs do), parsing (aka recognizing languages) and calculability are all the same.
Classical literature about these subjects include the Dragon book and the Cinderella book.