Because in this case, battle=fights. If it's going to be as loosely defined as you say, then pretty much everything with any kind of verbal or mental back and forth is a battle series.
Yakitate! Japan is merely a series of judged competitions. If they were throwing special types of bread at each other or shot laser beams out of them, it might count. Even with an unconvential medium, if it were to follow the general tropes, it could be considered a battle series. For example, if Kemeko DX's premise was more in line with
this pillow fight scene rather than it being a 1-off gag, it would be considered a battle series. However, that is not the case with Yakitate.