You notice it much more in the East than you do here. I know they demonstrate in the larger cities in Germany, so you do get the big rallies, but you definitely do not sense the reality of the NPD here on a daily basis like you do in the former GDR.
I think, like it said in the article, the largest problem is by far the unemployment in the East. The town I lived in had 20% unemployment and the following situation: Large porcelain factory employing thousands was closed right after reunification. West German investors came in and bought up factory buildings and other properties for very little money, then instead of bringing new industry into the area, sat on the properties until they were so run down the buildings needed to be torn down.
You have people who have only ever worked as calligraphers in a porcelain factory trying to find and IT job.

They don't have much of a chance. There are so many people in there early 40s who lost their jobs 15 years ago, haven't found anything in the East but because of family or other responsibilities haven't been able/weren't willing to move to the West. Now, with 40, their job applications are constantly rejected on the basis that they're too old.
The other big problem is that you have a large number of Eastern Europeans (mostly Russian, Ukrainian, Turmenistani, etc) who get their visas and are set up with a place to live in the East. Now, I know they do get some kind of compensation for having a great, great grandpa who was German- but it doesn't sit well with the locals. I think the attitude is "Why are they bringing all these Russians in and giving them all kinds of cushy kickbacks when we're here and can hardly get by?" They feel shit on, to put it bluntly.
Now, up until a few years ago, the goverment showered them with unemployment checks and Umschulungskurse (retraining courses). It was a short term fix to keep them floating by on welfare but offered absolutely no long term solution for the economic situation in the East. I could write volumes about the ineffectiveness of retraining programs for the unemployed since I taught in these schools for 5 years...

As you can imagine, the government ran out of money, drastically reduced the amount of schooling they were funding, and now everyone who's been in and out of retraining courses for IT-Systemkauffrau or whatever else for the last 15 years is sat on their sofas with no chance of getting another training course.
Anyway, I think people in the East have developed a "desperate times call for desperate measures" attitude. You not only see a much higher support of the NPD, but you'll also find a large number of people voting PDS. In fact, more people vote PDS than NPD in many areas.
The NPD gets more attention here than the PDS though.