哥哥 in this sentence means "I". It is an amusing way to say "I". It implies an emotion but I can't find a good way to explain it at the moment. If it is a young girl, she can say "妹妹" instead. But, sometimes, she might also say "姐姐" to show her maturity in a fun way. If it were me, I would add a "我" after it, for example, 姐姐我开的店 / 哥哥我开的店 /妹妹我开的店.... In that way, no one will get confused.

In my opinion ,"gege" in your sentence can be your own big brother or your elder male cousin or some one you are familar with and older than you .I hope it does make sense

in my opinion, it's his sister who said this sentence.Meimei 妹妹说的这句话。句子中的“我”，就是这个妹妹。

也可以是 親密愛人之間的稱呼 http://mypaper.pchome.com.tw/hintaiwan/post/1313921750

ge ge, da ge, jie jie, da jie ... just big brother, big sister in English I think.