Allow me to suggest something.
Go perform an analysis of every factor you can find about those pages, compared to sites that don't rank nearly as well: Inbound links, title, description, on page factors, internal linking, inbound anchor text, etc., etc., etc.
Once you've done that deep level of research and analysis, an effort fully justified by your interest in outranking that other site in the same niche, then come back here an explain/share what you have learned by you extensive research and analysis.
Maybe after you've exhausted all possible avenues of determining how to compete - and put up everything you've found for the rest of us to scrutinize - then maybe we can fill in some gaps.
On the other hand, maybe after you have labor for hours attempting to sort out "how do they do it" - and you run a few tests and learn that you can do it also - maybe then you might decide that it's not in your best interest to share and reveal whatever "secrets of ranking" that you learned, because after all, if everyone knows those secrets of ranking then everyone else will be jostling to knock your website out of its position.
Then it will be off to the research room to labor for some additonal hours to learn how to outperform everyone else, in which case you might then choose to not publicize what you have learned.
Here's the rub: The guys who really know how this stuff works are using lots of domains on lots of servers with lots of phony WhoIs profiles and lots of variety in everything they do. That's how this stuff is learned.
It's also learned by attempting to reverse engineer how someone else got lucky . . . or did not get lucky.
In either case, at most what you will find publicly available on forums is only the basics of SEO and yesterday's tips for success. The real worker bees are determining what move to make 3 steps ahead of where things are now.
So my advice is to get some additional domains on some different IP addresses and start to play around.