So you mean if an individual "X" murders a person "Y" ("Y" here is not a big political figure but a person with a different political ideology when compared to "X"), based on his political ideology then that individual is a terrorist?
In the above scenario all the elements that you mentioned are present.
Calculated use. Yes.
Use of Violence. Yes.
Gain political advantage or religious advantage. Political advantage, yes ( Based on my scenario ) and you might say that "Y" wasn't a big political figure so how's this a political advantage? The murder of that an individual sends a message to the society nonetheless.
Invokes fear in minds of the society. Yes.
By your definition a simple homicide which was politically motivated is an act of terrorism.