That is a very narrow definition of terrorism. So narrow it would exclude terrorist actions based on race, like the shooting of 9 Black people in Emanuel A.M.E. Church in Charleston, South Carolina. By his own words and confession, the shooter killed them because he hates Black people. Same with the shooter who killed people at the Buffalo grocery or the white guy who massacred people at Walmart in El Paso. These men didn’t have political aims. They wanted to kill and cause terror to Black and Hispanic people. They didn’t aim to cause any political change. Just hurt BIPOC. It would also exclude religious terrorism.
You also think we can’t use the word terrorism until we know the underlying motivation of a crime. Which is just bullshit. We often never know the underlying motivation.
And yes, this is technically vandalism. But that doesn’t preclude it from also being terrorism.
From the FBI website
Domestic terrorism: Violent, criminal acts committed by individuals and/or groups to further ideological goals stemming from domestic influences, such as those of a political, religious, social, racial, or environmental nature.
US law, 18 USC § 2331(5), emphasis mine, states:
(5) the term “domestic terrorism” means activities that—
(A) involve acts dangerous to human life that are a violation of the criminal laws of the United States or of any State;
(B) appear to be intended—
(i) to intimidate or coerce a civilian population;
(ii) to influence the policy of a government by intimidation or coercion; or
(iii) to affect the conduct of a government by mass destruction, assassination, or kidnapping; and
(C) occur primarily within the territorial jurisdiction of the United States.
Political motivations do not enter into it. If the illegal act was dangerous to human life and was intended to intimate a civilian population, it doesn’t matter why the terrorist wanted to intimate, cause fear, or cause terror. That definition is broad, as discussed by the ACLU. The ACLU does have a point on that.
Vox has an interesting discussion on whether the insurrection on 1/6 was terrorism. Domestic terrorism definition: Does the US Capitol attack qualify? - Vox
Edited to fix the odd formatting.