Oh good lands, I've never seen a case of popeye that bad.
Wow. Okay, first, odds are we're dealing with an internal, localized infection. In the words of The Betta Handbook, "the bacteria in the epithelial linings in the head produce gases that force the eyeball outward." According to this book, the only treatment for this is a gram negative antibiotic issued via medicated feed and it doesn't always work.
Now, I have to say that I'm not 100% sold on this theory about only medicated food being able to treat it. I would suggest you use Seachem Kanaplex, which is one of the few antibiotics that readily absorbs into the system through gills and skin. It can also be used to prepare medicated food if you want; there are instructions on the packaging.
Now, the downside is Kanaplex is hard to find in stores and usually has to be ordered online. :(
I would also recommend adding API Erythromycin because I've also read that a lot of eye infections are actually gram positive bacteria and that erythromycin is effective in treating this.
There is a strong possibility that he will lose the eye but as long as the resulting injury doesn't get seriously infected, he should be able to recover and will be able to live just fine without that eye.
How is his behavior otherwise? Will he eat?