Yes, it means fattie but this could be a cute nickname but only when the person that you call 뚱땡이 is really close with you and you should check if the person is not stressed about being fat. Sometimes I call my fat friends 뚱땡이 or 뚱띵이 or 똥땡이 as a cute nickname. The proper word is 뚱땡이. Some people don't want to be called that name, some people don't mind it much. But make sure you are not officially call someone 뚱땡이.

안녕하세요, 미나 씨. The correct spelling of the word is 뚱땡이, not 똥땡이 and its meaning has nothing to do with cuteness.^^; Some people may accept it as a joke, but some people may get offended, so please be careful when you try to use it. Hope this helps.