Your role here is as a de-facto parent. You clearly care about the boy and you should focus on that - you have a huge role to play, but you are not a language therapist/child psychologist/occupational therapist. Your job is to get the little guy the services he needs and be prepared to be stubborn and insistent that he gets them. And there will be lots of "homework" to do that will keep you busy once you get that.
Early intervention is key, so getting into the system and getting access to the necessary services is your top priority. Accept any and every appointment that comes your way. Also, you need to be in it for the long haul - my experience is that it's a case of incremental progress over long periods rather than giant leaps. You may at some point feel that this is over the the top, or that his issues aren't that bad compared to other kids that you encounter. Forget that thought immediately.
Like others here, I would not generally suggest looking for hacks. But one thing that really works is probably something you're doing already - playing. Let the child lead, talk constantly to describe what they are doing and occasionally ask questions. That's a very basic description that should get you going, and once you get access to the services you need, you may be able to find out more (some sort of parenting course for kids with needs is usually part of the process).
Finally, just keep doing what you're doing, but also look out for yourself in all this. Good luck!