I have been through that same situation and found that stepson would get bored at our house and try to start stuff by teasing the little ones (he thought it was funny). There was about the same age gap as yours and we just didn't have enough to keep him busy--his Dad worked a lot so he felt 'dumped' with me and the girls. He was also a video game addict--(his mom gave him unlimited time) and he thought it was funny to let the girls play with him, but then put the 'cheats' on so he would always win, etc.....just crappy mean stuff but then they got wise and wouldn't play anymore 
. He wasn't around enough to make real friends in the neighborhood, there was a kid next door but they didn't get along well--again, stupid stuff like trading baseball cards, then being unhappy with the trade and starting stuff. I finally put my foot down with hubby and said 'you need to make plans with him while he is here---one on one boy time!'. Even just going outside to toss a football around or go to a high school game helped a lot. Now they are all grown and gone but there are still stories that come out once in awhile---he taught them how to shoot spitballs at the dining room window, etc etc......I think a lot of it is just the 13 year old in him.....he has to just grow out of it.
. He wasn't around enough to make real friends in the neighborhood, there was a kid next door but they didn't get along well--again, stupid stuff like trading baseball cards, then being unhappy with the trade and starting stuff. I finally put my foot down with hubby and said 'you need to make plans with him while he is here---one on one boy time!'. Even just going outside to toss a football around or go to a high school game helped a lot. Now they are all grown and gone but there are still stories that come out once in awhile---he taught them how to shoot spitballs at the dining room window, etc etc......I think a lot of it is just the 13 year old in him.....he has to just grow out of it.