Fermentation does not require vinegar! Fermentation is the natural process of turning sugar into vinegar. Just for in case you're interested. This is not fermented vegetables. It's pickled. You can't have fermented pickles in vinegar. It doesn't make sense...
I highly recommend not trying it outside of the refrigerator. Even if you water-bathed your batch for a long time, the oil can insulate bacteria in small pockets, and this recipe has a LOT of oil.