Why do people do this? Are they trying to engage others in conversation?
I have known people like that, but not enough to support any general theories about them. My impression from the few who did know is that they were just flushing out their thoughts, and didn't really care whom they flushed them out to. For the particular people I have in mind, then, the answer to your question is "no". Far from engaging others
in their conversations, they were essentially talking to themselves, or thinking aloud.
How do I deal with this?
In the short run, I make a sincere-looking face, nod a lot, and interject the occasional "oh, really?", "you're kidding, right?", "yeah, tell me about it", or "I totally agree with you". No need to listen to what they actually say---with some practice, you can tell from the inflection of their voice which interjection is expected. So much for the short run. In the long run---meaning if it goes on for longer than I care to put up with---I pretend I have somewhere else to be, and discretely excuse myself.
Does this aggravate anyone else, or is it just me?
It does get on my nerves as well, but I can see how this would be especially aggravating for you. When you're hard of hearing, you need to make an effort to listen to people. And when this effort proves not worth it, time and time again, it must be wearing you down.