At this point, it's very hard to get a finance internship anyway, so don't let that stop you making the most of the Yahoo experience. Certainly you should do the internship, as Andy says it has a lot less value, but it still is good.
First up, you need to hedge your chances of not making it into sort of finance job you want by building your options in the IT industry.
But Yahoo is a brand, and these have several layers of value.
As a headhunter, my preconception is that that you had to beat a lot of your peers to get this job. We like to see that sort of thing, it says that someone who knows your game thought you were much better than a large % of people who play it.
There are two main paths open to you in the medium term.
First is the classical quant route, where you will be competing with people who've done more of the 'right' sort of maths, and you are right to compensate partly for this with better programming. But you will still need that sort of maths.
This is the most liquid market, and where most people in this game end up.
But you are mildly well set up for a more specialist job at a hedge fund or proprietary trading operation, either standalone or in an IB.
There is good money to make from looking at vast piles of data trying to work out what is going on.
But it's more specialist, which means that there may be no job for you, or several good offers.
You appear to be thinking of quitting at MS level, and that's probably sub optimal, unless you really hate your PhD. A MS in CS makes you a quant developer, or rather someone who can learn to be a QD, which is an OK job, but possibly you can aim higher.
If you are at the stage of choosing your PhD topic, then I would give serious thought to using and building skills to identify signals in series of price data. To be done properly you'd understand 'market microstructure', not technical analysis.
