Some quick thoughts, mainly to suggest a deeper analysis may be warranted....
How old are the domains? How long have they been in the serps? How long have they been above you?
When did drop in your rankings occur? Did just you drop, or was there a widespread change?
1) TBPR - very approximate ballpark indicator at best, often misleading by itself. It is never current, eg.
2) number of incoming links is never by itself a good indicator. Where, eg, are the links from? What is their quality? What is the relevance of the link source pages? Factors further upstream? IPs? There's a difference in the two tools... Majestic is generally fresher, eg, by a fair amount.
3) beating strong sites... but on those strong sites we don't know about the strength of deep pages. As you note, it's obvious on one-page sites that links must be going to the pages themselves, rather than being distributed through a navigation system of unspecified quality.
4) drop of your competing page... You're looking at it as all about PR and links, and that may not be the case. Drop could be attributed to how Google has re-evaluated your inbound links and to upstream factors affecting your inbound link quantity... and (PS) as Sand says, about content.
I can understand more direct links leading it to beat my site, but given it beats almost everyone, the only explanation I can think of is that the keywords in the domain work.
Not disagreeing with this... just suggesting there are multiple factors.
If we see a lot of one-page sites ranking, it's likely to be a weakness in the algo, currently being exploited, that Google will need to address.
Are the one-page sites sufficient to address all of users' needs for the query/queries for which they rank?
Are they ranking for just one phrase, or for a range of phrases?