There is no accepted theory. There are indeed multiple defining differences between the 6th title and all others including earlier titles: the first Windows title, the inavailability of detailed backstory (thus a fertile ground for derivative works), the only title with obviously Western characters and so on, but none of them seems crucial for the eventual popularity. If you ask me, my guess is that it was just a pure luck.
The popularity of Touhou series didn't reach the Western world for a few more years. The tipping point in Japan is thought to be the 8th title (Imperishable Night in 2004) and I believe it took another 3 or 4 years for Touhou to be reasonably popular outside of Japan; the earliest known "Touhou hijack" in 4chan was around 2008 for example, and as a South Korean, I myself learned of Touhou in c. 2006 via a doujin music. The 6th title then became popular among other titles in the series somehow.
