I think you're thinking too much about numbers. Outside of its legal definition, an ongoing conflict between two groups can be considered a war. I think its rather about duration (as opposed to one instance of fighting, which would just be a battle or conflict) rather than how many are involved.
Then you don't understand chimp culture. Chimps do seriously "go to war" against other tribes. You have to remember that humans killing humans for the sake of "I just don't like you or your friends" is not the norm in the animal kingdom. So yes, it really is a "chimp war", despite their relatively small numbers.
I'm pretty sure they're objecting specifically to the "relatively small numbers" part; I probably wouldn't call a conflict involving only 14 humans a "war" either, culture or no culture.
That's just the size of a chimp "nation", this is like arguing Luxembourg can never go to war because "It has a current strength of approximately 450 professional soldiers" which is obviously far too few for any real scotsmans war.
My first thought was about Dunbar's number too, but Dunbar's number for people is something like 100-120... yet we're still able to field 10,000-man strong divisions, expeditionary forces, etc.
Chains of Command follow the Hub and Spoke model. I'm pretty sure if you break it down the number of people an individual in that structure has to care about is somewhere between 30 & 60...leaving them room for friends and family.