Give me your opinion
You must honor the bet. I had this exact same situation happen to me. I ended up losing my girlfriend, but you have to honor the bet, otherwise it meant nothing in the first place. If the stakes weren't real it invalidates the entire fight. If your girlfriend made the bet and lost that's her issue. She should realize that when making a bet like that you need to be able to fight for you mans honor.
It may seem strange, foreign, and even wrong initially, but in my case I found the sex with the woman who destroyed my girlfriend to be absolutely mind blowing, it was the best I've ever had. The atmosphere and circumstances just combine to make it extra wild.
So basically if you allowed them to fight after the decision was made then yes you should follow through. I'd imagine their are some girls out there who actually have honor and would respect you more for sleeping with the victor to honor the bet. In order to respect themselves they would willingly accept the fact that you have to sleep with the victor. No matter how emotionally devastating it is to them.
It's not even like the guy always leaves after the sex. The sex might have been terrible, and even in cases where it was amazing, like mine, I still told my girlfriend I was willing to stay in the relationship if she was. Unfortunately, she didn't think before she made the bet, which is why she just couldn't deal with me sleeping with another woman.