Surely it does? As running burns "body fat" and your stomach is a big part of that!
Afraid that's not how it works.
Running doesn't burn bodyfat, in fact exercise alone doesn't. It's how your body chooses to use it's fuel for energy that dictates these things. And a lot of the fat burning takes place after exercise (up to 24hrs in fact).
Eating the right things, and how your hormones behave to the different stimuli is the thing to concentrate on - however that gets far too indepth.
As BBx, myself and others have said, a combination of exercises, HIIT, and a structured diet (which is the most important for fat loss) will put you onto the path of fat reduction.
You could run 100km (just making a point - 100km would be mad

) every day and still hold fat if you're not eating the right amounts, and if your body is able to cope with the exercise, your body will not be using fat for fuel - you have to get your heart into the fat burning zone, but also think about how you refuel your body. If you become uber fit, your body will cope with the stress of running easily - that's why programs such as HIIT, and doing some anaerobic exercises are actually much more beneficial to fat reducing, or at least calorie utilisation. There's a sequence for how your body fuels itself for exercise - which is why a lot of steady state cardio experts eat a lot of carbs as it boosts their glycogen levels reducing the time they are running depleated.
Diet will be the main factor, but a variation of exercises will help accelerate it. Of course, running will use calories, and you will shed weight (not necessarily fat) if your calorific intake is lower than your output - that's just basic fact, but most people are interested in retaining muscle tone whilst reducing the fat they don't want. THAT, is a lot more involved.
It doesn't have to be that complicated though - eat the right foods, do some varied exercises, and that's it really.
Of course if you run lots, and just don't eat lots and get the balance right, you wont lose weight or gain any, and a lot of fun/professional/amateur runners are slim and low bodyfat as they have got their calorific balances just right.