I'd say it's symbolic, but not combinatorial. Tldr: it looks a lot closer to symbolic than to connectionist, but it seems a promising new approach within symbolic methods.

What we call symbolic AI usually makes inference by exploring the space of possibilities generated by recombining the basic symbols of a (fixed) domain language.

Gärdenfors approach has a lot of this, in that it has a symbolic representation of data, a well-defined set of symbols that stand for objects in the observed domain (animals, in the example given); additionally, each symbol has a numerical value which represents how much of each property the object possesses.

This is somewhat similar to the knowledge systems of the 70s and 80s for incomplete, approximate rule-bad reasoning. But those were problematic because it was very difficult to do reasoning with their numerical values. When combining facts within the database, the respective combinations of their numerical values often had nonsensical meanings. The algebras used in those systems were not a good fit.

If Gärdenfors is right and concepts can be treated as mathematical spaces with convex regions, his approach could solve some major problems of those systems that made them impractical, and maybe bring them to prominence again.