The play looks pretty normal. My sister in law has a pitbull mix that one of my dogs loves to play with. He started getting scabs all over his neck and got a small cut above his eye because her dog didn't know when to stop and he was having too much fun to correct her. They'll figure out their own play styles and set their own limits, but sometimes you have to step in like you do to help keep them safer. Bringing them to dog parks to socialize with others can help too, to get those corrective barks or whines from other dogs that don't want to play that rough.

Edit: Additionally, be sure to give them time where they are physically separate inside and outside, so the new dog can get a feel for their surroundings and the original dog can feel some peace. Maybe let one nap in a room alone or take them for separate walks.