Here's my analysis on the entry:
The description is occasionally used - and in this case correctly - to refer to those who maintain that they are skeptical of things such as the facts about global warming., evolution or AIDS. In this case the word is simply a synonym of denialism, as there is a vast amount of real evidence which is simply ignored by these pseudoskeptics.
All of these are things that the establishment says. While I agree that the phenomenon described above are real - global warming(even though I think it's exaggerated a lot), evolution(though I'm not convinced it was entirely natural. Intelligence, for example, is a weird phenomenon. A cockroach would have much more evolutionary advantage over us. We're just not equipped to survive in the wile), and AIDS. It should be taken for note, because it suggests that this article is more about establishment defending, not about properly talking about pseudoskepticism.
It should also be noted that real skeptics are always prepared to change their positions based on the production of real evidence, such as in the case of Einstein's Cosmological Constant - thus making them immune to the accusation of pseudoskepticism.
 Usage by woo promoters
It is perhaps more often used as a loaded term by promoters of woo to dismiss skeptical criticism of their beliefs as unfounded. Some woo-promoters maintain that demanding evidence before belief is an extreme position, and they feel that we should all be agnostic about, well, everything until it has been positively disproved. Given the difficulty of absolutely disproving even the most absurd hypothesis they then go on to maintain that all those who ask for evidence before belief are "pseudoskeptics".
This is a pure strawman. We never said that demanding evidence before belief is extreme. What we say is that after we've given you evidence, and you still deny it and say there's no evidence without even a basis to deny it, would be pseudoskeptical.
Consequently, these woo-promoters will try to claim the high ground by describing themselves as being "open-mindeded" in comparison to the allegedly closed-minded members of the scientific establishment who demand actual evidence before accepting the woo peddlers' pet beliefs as anything more than bogus at best.
An example of ad-hominem. Furthermore, the word "actual" before evidence suggests an easy basis to deny evidence. More specifically, it allows for an easy double standard.
As an example, SCEPCOP maintains that: pseudoskeptics "will never accept a paranormal [explanation] that includes metaphysical dimensions because they believe it's impossible."  It would be interesting to see what they think of the scientific method and methodological naturalism.
 Skepticism and agnosticism
The scientific method isn't about debunking everything that doesn't fit with your beliefs. Otherwise, I could call the global warming a hoax because I could explain it with a inverse correlation with pirates.
In any case, skepticism and agnosticism are not necessarily exclusive positions. If somebody maintains that there are invisible, undetectable fairies at the bottom of their garden, there is no way to prove that this is not the case - though equally there is no supporting evidence. There is an infinitesimal possibility that these beings exist and accordingly it can be argued that "agnosticism" towards the claim is the appropriate position. However, being agnostic about a belief does not mean that there is a 50/50 possibility of its being correct - it merely means there is a possibility. In this case, the improbability of the assertion coupled with the lack of evidence justifies our being extremely agnostic about the assertion; in fact a position of such extreme agnosticism that it is, for all intents and purposes, indistinguishable from disbelief.
Again a pure strawman analogy. See Winston's treatise page for for more information. More specifically, there is way more evidence for paranormal events than invisible fairies - including scientific experiments from credible sources and a ton of anecdotes.
Sorry, but many believers try to consider possible mundane explanations before coming with a conclusion. Furthermore, we aren't omniscient deities, so we shouldn't be quick to judge a position as delusional or nonsense, even if it's backed up by evidence.