Hence, a subset. No one is claiming competitive usefulness is the be-all, end-all measure of whether a Pokemon is loved or not. The prime example of this would be Charizard; it was absolute rubbish competitively in Gen 4 and Gen 5, and thus wasn't used much at all, but there's not a person on earth who would claim that Charizard is unloved. However, whether or not a Pokemon is loved is not a black and white, yes or no answer. Popularity exists on a spectrum, and how much a Pokemon is or isn't loved can be debated based on a number of factors; general public reception, notoriety, appearances in anime/movies, competitive useage, emphasis within the main games, etc.But being unused compeitively does not automatically constitute being an unloved pokemon, just as being used competitively does not automatically constitute being a loved one.
Competitive play is only a portion of the whole spectrum regarding a pokemon. I do understand that competitive prowess is a valid reason for many to love a pokemon, but to make it synonymous with loving a pokemon just seems out of touch to me.
However, competitive usage is just the easiest point to prove. Simulators have usage statistics, Battle Spot keeps records of the most used Pokemon, and VGC has teams tracked to see which Pokemon are most common. You can easily figure out the most used Pokemon, and usage is an objective fact (and only usage I mean, not to be confused with competitive usefulness which is subjective), as opposed to something like how well received a design is, which is wildly subjective. Whether that's enough to determine if a Pokemon is loved or unloved depends on the person interpreting it, since the entire concept of "loved vs. unloved" is subjective as a whole. There could be some hidden cult that numbers in the thousands and worships Farfetch'd and Dunsparce for all we know, but if we're not directly observing those people who love those Pokemon, then the perception is that they're unloved. But it's just that; a perception.
tl;dr - Competitive use is a factor that can't be ignored or discredited. However, it has to be weighed against all the other factors as well.
Masquerain would be a good example of a Pokemon that's unloved for a multitude of reasons across the board. It disappointed a lot of people by losings a unique Bug/Water typing to become a generic Bug/Flying type, it's not great competitively, and its role in the anime was fairly minor.