My gut feeling is that this is very unlikely to be negative SEO. Frankly, it's still very rare, and most cases that are assumed to be negative SEO turn out to be much more complicated. One oddity here is that I'm not seeing a clear penalty-like scenario. You're talking about a very specific case of multiple pages showing up for a single query. This could be as simple as Google tweaking their domain crowding settings. I see this frequently - one day, a single domain will get multiple listings; the next day it will get one. If you look at thousands of SERPs, this actually happens every day.
This could indicate Google saw a change in your signals or signals related to your brand name, but it's unlikely to be due to negative SEO. It's also, honestly, not a huge issue, for the most part. You still rank #1 for your brand, and your brand is just one query. If Google has decided to not show multiple pages from your domain, this may be beyond your control and have little or nothing to do with your SEO efforts.
I do also share Dirk's concerns. A lot of the internal pages are being cached with very little text - Google is indexing them, but the text-only content is showing up as just a few menu items. These pages are going to look thin, and they may be running into some quality problems. This could cause them to compete with each other and fall out of some rankings. While Flash can be used successfully, the implementation here is part of the problem. The load times could also be causing you some issues. At best, it's creating obstacles.
At first glance, your link profile also looks pretty weak. You have a ton of free PR sites and web directories. In small quantities, these are fine, but when they make up a huge swath of your profile, you're getting into danger territory. When I see things like "free link directory" over and over, I start to worry. Add that to technical and on-page problems, and now you're compounding the issues.
I'm also seeing that some of the "links" are actually 301-redirects from a very long, exact-match domain, that you've redirected to the site entirely. I'm seeing a number of serious quality issues in your link profile, to be brutally honest.
I don't think the problems here have anything to do with the competition. I think you have to take a good, hard look at both the technical state of the site, the overall content quality, and the overuse of low-quality link tactics.