Is the IP domain in Ireland or somewhere else. I think that is one of the things that ensures that you are on the "pages from ireland" so you are ranked higher as you are from ireland. The reason for "the web" being so low is that that you are against all the rest of the world. AFAIK
I've got pages that do the same, and I'd suspect it's down to the linkage anchor text, try an allinanchor:Keyword search on G and see where your site/competition turn up, they should roughly mirror the positions in the organic results.
Take Huntforproperty.ie, you use "Irish property" in you sig here so:
allinanchor:irish property - 14
The web - irish property - 13
strip out the non-Irish sites and in the Pages from Ireland results you rise to 10th.
Well the domain is a .ie, registered with Hosting365. I appreciate your point but it doesn't explain why all my competitors (.ie domains) are ranking in the top 10 for the same keyword. I do think that "the web" searches are localised on Google.ie. For example: this search doesn't suggest that Red Fly are ranking number 1 worldwide on Google. Just on Google.ie.
Was looking at GUK results for web design, they vary significantly from the allinanchor results but most of those "unexplained" sites feature prominently on allinanchor variations such as website design or web design UK.
Looks like they may be factoring in close variations in allinanchor results, possibly as a means of returning a higher number of regional results while still maintaining their "quality criteria" or possibly as an anti Google bomb measure.
Anyway, to keep the thread on topic I'll PM you if I find anything of interest...
Haven't looked at on-page stuff yet, trying to discern some kind of pattern in the linkage first.