At that level of generality, a lot of things are political since one of the definitions of politics, according to Merriam-Webster [1] is: "the total complex of relations between people living in society". Does this now mean that if I hang out with a friend, this may, under this very broad definition, be considered political? Is your suggestion then that me asking my friend to hang out is in some way an incitement to violence?

I feel like these sorts of categorizations based on broad definitions of terms almost never arrive at anything substantive. Categories are generally always fuzzy on the boundaries and using strict definitions to demarcate them is a complicated process (see, for example, the Judicial System).

Also I find this opinion preposterous because the incitement to violence in this instance has nothing to do with "political discussions about what the state should do". The President certainly did not have a political discussions with his supporters about what the state should do - rather, people in a state voted to decide who should lead, according to rules that ostensibly most of the citizens agree with, which the losing party then tried to contest by trying to wield violence themselves.

[1] https://www.merriam-webster.com/dictionary/politics