This is how the DOD defines terrorism:
The calculated use of unlawful violence or threat of unlawful violence to inculcate fear; intended to coerce or to intimidate governments or societies in the pursuit of goals that are generally political, religious, or ideological.
This is the definition of terrorism under U.S. law:
(2) the term “terrorism” means premeditated, politically motivated violence perpetrated against noncombatant targets by subnational groups or clandestine agents;
This is an excerpt from Ted (the Unabomber) Kaczynski's manifesto:
We therefore advocate a revolution against the industrial system. This revolution may or may not make use of violence: it may be sudden or it may be a relatively gradual process spanning a few decades. We can't predict any of that. But we do outline in a very general way the measures that those who hate the industrial system should take in order to prepare the way for a revolution against that form of society. This is not to be a POLITICAL revolution. Its object will be to overthrow not governments but the economic and technological basis of the present society.
This is from the Al Qaeda manifesto titled "Why We Fight America":
What happened to America [on 9/11] is something natural, an expected event for a country that uses terror, arrogant policy, and suppression against the nations and the peoples . . . America is the head of heresy in our modern world, and it leads an infidel democratic regime that is based upon separation of religion and state and on ruling the people by . . . laws that contradict the way of Allah. . . . [Therefore], we have the right to kill 4 million Americans - 2 million of them children - and to exile twice as many and wound and cripple hundreds of thousands. Furthermore, it is our right to fight them with chemical and biological weapons . . .
This is (in part) Joe Stack's justification of his actions of February 18th, 2010:
I know I’m hardly the first one to decide I have had all I can stand . . . I know there have been countless before me and there are sure to be as many after. But I also know that by not adding my body to the count, I insure nothing will change . . . I would only hope that by striking a nerve that stimulates the inevitable double standard, knee-jerk government reaction that results in more stupid draconian restrictions people wake up and begin to see the pompous political thugs and their mindless minions for what they are. Sadly, though I spent my entire life trying to believe it wasn’t so, but violence not only is the answer, it is the only answer.
Each of these excerpts represents the mindset of an individual or group of individuals who carefully thought out what they were doing and why they were doing it (premeditated, calculated). In each case they advocated and/or perpetrated and/or threatened unlawful acts of violence to intimidate governments or societies in the pursuit of goals that are generally political, religious, or ideological.
Clearly the Dept. of Homeland Security is full of beans.
Now what effect does the DHS's statement have in broad terms? Well, if joe Stack is not a terrorist, it becomes less of a political liability for Republicans to (while deploring the act itself) sympathize with his frustration toward the tax code and assert that the Democrats and their big government schemes are driving the people to extreme measures. Furthermore, it seems unlikely that the Democrats will offer much pushback on the topic of Stack's status as a terrorist since if people start seeing him as a terrorist it means that the Obama administration has allowed a terrorist attack on American soil and is therefore an ineffectual protector. The real bummer is that this will probably work very well for the Repubs.
This also illustrates why humans in general are idiots and don't really deserve a future.
Update: As usual, Glenn Greenwald has a bunch of very intersting things to say on the topic.