Curious thing, it's always the right pedal, isn't it? I have a bin full of left pedals that are still okay after the failure of the right one from each pair.

But as to your pedal, you may be able to tighten it still. The nut you see is a locknut; take it all the way off. Next you'll see a washer with a tooth on the inside, which registers in a groove on the axle. Take that off, too. Now you see the cone, which is threaded onto the axle. You can turn this; that's the adjustment you want. Tighten it a little, but leave it a bit looser than you want. Now put the toothed washer back, and the locknut, and finally tighten the locknut down all the way. This will press the cone against the threads, and hopefully take up that last bit of looseness you left. If it's too tight now, or too loose, repeat the process until you get it right.