Playing football or violin is a different action than playing with something. When you play with something that means just playing with it like a toy. It's hard to describe exactly, but playing with the violin would just refer to using it as a toy, but nothing to do with actually playing it as an instrument. Likewise playing with food or fire is just having fun with it, not using it in any way.
You can play games, instruments, sports, etc, but playing with those things refers to just using them as a toy, not really a specific action with them.