This has a lot of potential to be a great new feature. I only have a few things:
Amount of PK points could depend on the level difference between players (for example: if your combat level is 100, you only get a few points from killing someone with combat level 80, but lots from killing level 120).
To reduce boosting, could require a certain level to obtain points, this combined with the first suggestion could pretty efficiently stop boosting.
You could only obtain points from killing the same player once a day.
The shop could be a combination of rare cosmetics and useful weapons/armor/tools.
You could buy titles from the shop, the titles would only last ~30 days, and after that you'd have to buy new one, title would be hideable in the settings.
Overall a great suggestion