In my experience with working with Parse, I don't believe that it's the correct solution for your needs.
You may get things up and running at first, but as you try to scale your application, you're going to need to ramp up your servers (and cost!) greatly to handle so many requests. Parse's pricing is based on your requests count for the month. Imagine how many requests you expect one user to make in a month. Now times that by 1000.... Not very scalable, huh?
Now I don't know much about xmpp servers, but I've heard from some colleagues that applications like WhatsApp are using Erlang and TCP servers (just like Call of Duty) to handle message requests. In fact, here's an article that talks about the logistics of WhatsApps technology https://www.erlang-solutions.com/about/news/erlang-powered-whatsapp-exceeds-200-million-monthly-users
Best of luck!