Google uses around 200 factors to determine how to rank sites for given search terms, so there could be many reasons why one site is higher than another for a term like "office supplies".
A lot can be influenced by inbound links, but to analyse the quality, not quantity, of inbound links of a site can take time, so I wont comment on this. I will however comment on a few more immediate issues:
1. Your competitor has
15000 pages of office supply product information on their site, whereas you have
100 pages - again size/quantity isn't everything, since the number 1 site has
1100 pages , but content is important
2. Your competitor has one of the search term's keywords in their domain name whereas you have none, (the site that is number one on google has both and just that)
3. With your competitor, there may be some jiggery-pokery going on with not just the one site but also with another site ukofficedirect.co.uk which at first glance looks very similar but has more history going back to 2002, and a whole host of other similar domain names like ukofficedirect.com going back to 2001
4. Your competitor, according to
yahoo, has a lot more inbound links than you have mentioned, and not just to the one site but to its other sites too (which may in turn help ukofficeonline). The number 1 site on google has less inbound links which can demonstrate that it is not just about quantity but quality.
5. I really don't know whether staples are inadvertently shooting themselves in the foot with this, but I have noticed that staples are listing their competitors at the bottom of their
page which might be helping the site which is no 1 and ukofficedirect (which may in turn help ukofficeonline)
So to answer your original question... no, it is never that easy.