I think that that rhetoric works in a perfect world where games are all completely unique in more varied and nuanced ways. Right now, however; I still think its too soon to do away completely with comparative scores because games are still, for the most part, a comparative experience.
I will not argue that the content of the review should take precedence above any binary affiliations we attach to the game; however those particular binaries can be useful to gauge the chism in excellence between 2 similar games. Let us say, for example, you are attempting to make a decision between BF and COD for the first time. If you were to read both reviews for the latest iterations and were unable to come to a definite conclusion as to which you would rather have purely based on the content of said reviews; a well aligned binary system based on numbers that are transparently understood could give you a better idea of what you want most out of the game. Obviously this logic presupposes that the system is not inherently flawed and that you have various categories to assign instead of one overarching score. However I still think there is merit to having a tangible way to relate the excellence of a game on a scale that isn't entirely at the mercy of the prejudice of the writer.
With regards to the Eurogamer system; I think that having only 3 categories is somewhat flawed in that you are assuming that every game can be encompassed within those 3. What about games that are essentially terrible but are still engaging in some way. What do we score those? Or games that are feats of technical marvel but are so contrived in their presentation as a game that they are barely playable? Also this makes it very difficult to draw comparisons between similar games if the both carry the exact same , "Recommended", tag line.
In short I don't think the problem is the numbering system. Rather that we have been asking the numbering system to do the wrong thing; that being taking the place of the review. I think the 2 ideas should exist in complements to one another. I think that it doesn't have to be a zero sum argument. We can have insightful reviews and yet still have insightful numbering system to better condense the ideas put forth in the review instead of assuming that one fundamentally detracts from another.