There was talk a long time ago (near launch) that SE was planning to implement some add-on support in the game, but I haven't heard anything about it in the past year or so. It seems like the plan may have kind of got pushed to the back burner and left to die there, never exactly canceled but never acted on either.

Without actual add-on support in the game, no third party apps are allowed to interact with the game software. (Not allowed to doesn't mean that none can, but any that do are a ToS violation.) As for DPS parsers in particular, though, the game does allow an option (at least on PCs) to dump the chat log to text files, and third-party apps that do nothing but look at those text files without interacting with the game software itself are allowed. The log from a chat tab that records all the battle info can be parsed out to a half-way decent (though not perfect) DPS estimate.

(You're not supposed to talk in-game about what any parser gave as DPS numbers, though. As near as I can tell, this appears to be because SE doesn't want to be placed in the position of trying to figure out whether you got those numbers from one of the legal parsers or illegal ones.)