I believe you are conflating "having a political desire" with "...an implication here that there is some form of organized political desire that you are acting to further.."
If a man loved Nazis in 1938 and blew himself up in Times Square?
Not terrorism. There's no use of stealth in a pre-meditated way to instill fear to enact some political change. It's just some Nazi schmuck blowing himself up.
Apologies if I'm responding to what I think you are saying instead of what you are, but fuck me. There's a huge difference in talking about what people feel and what they do, right? I feel a bunch of damned fool things, Never thought that this was some sort of topic for political debate.
The problem is that a bunch of disparate unorganized attacks can have the same effect as a coordinated intentional terror campaign. At that point, you have to decide whether terror is defined by intent or effect.
One Nazi in times square? OK, not terror. A dozen Nazis all across America, even if uncoordinated? Terror.
I default to intent but am also liberal in allowing effect to stand in for intent.
In that case, I would argue that this attack fits your definition of terrorism.
The political ideology is white nationalism clothed in Islamophobic garb.
The immediate political desire is, in the attacker's own words, "get out of my country!"
It's hard to argue that killing someone (and by extension making people like them fear for their safety) is not a deliberate and planned way of getting "them" -- both the individual and the group that individual supposedly represents -- out of your country.