My step son was 6 when I first started dating his mother, he was much like you describe her son. I get that it bothers you, you’re used to your two girls (which are girls and yours) but he’s a young boy, completely different. Don’t let that be a barrier to moving forward; for now, let her take the responsibility for him, as long as he isn’t “harassing” your girls, not your problem. If you two progress, she will likely be ok with you being a parental figure and in my experience, boys respond well to a father figure. It’s not always easy, but you will gain his respect and he will likely start following the example you present of how a male acts.
My best suggestion fo now, tire him out.. throw a football (make him run for passes), teach him how to catch/hit a baseball, challenge him physically and he will start to focus.
M - 9 1/2 years 5/5/16 - Bomb drop - 3 week EA 10/31/16 - We sold house 01/10/18 - D Finalized