According to your description, these activities are harming your site. Your first duty is to your community, so yes, you should step in.
You have rules, which he has not broken, and you probably have disciplinary measures (such as limiting participation) that can be applied when rules are broken. He hasn't broken rules, so I advise against jumping straight to those disciplinary measures -- he'll cry foul over that and won't obviously be incorrect. But you can talk to him, and you can start to lay the groundwork for future discipline, should it be needed.
In the situation you describe, I recommend opening a private communication channel with him (whatever is normal or most effective on your site) and issue a warning -- tell him that this behavior is disruptive and must stop, and if it doesn't you will take further action. Also stress that you value his contributions (if you do) and want to find a peaceful solution. If you have anything like a user agreement or code of conduct that covers these kinds of behavioral issues, remind him of the key points. If he tries to rules-lawyer you, firmly point out that the needs of the site are paramount. Do make it clear that you're not kicking him out; you want to keep the positive but stop the problem behavior.
If you are part of a moderation team, you should consult your fellow moderators first so that you are all in agreement about the plan (including what consequences will follow if he doesn't stop). Since you're stepping a little outside your site's written rules, make sure you don't surprise your peers. But it's expected that sometimes you will encounter situations not strictly covered by your rules, because users will always find new and clever ways to keep moderators on their toes.
I'm a moderator on several Stack Exchange sites, the longest for two years, and I and my fellow moderators have handled some "novel" situations. I've found that if I act with integrity, in a way I could explain in public if challenged, and with a focus on the needs of the site, the community will generally support my actions.