A non-species-specific, non-bio-chauvinistic definition of cognition?

In recent developments, the enactive perspective has started to advance on the intimate connection between the concept of autonomy and sense-making, the normative engagement of a system with its world (Varela 1991, 1997; Weber and Varela 2002; Di Paolo 2005; De Jaegher and Di Paolo 2007; Thompson 2007; Di Paolo et al. 2008). The latter is nothing less than a strong candidate for a widely applicable, non-species-specific, non-bio-chauvinist definition of cognition. (Di Paolo, 2009, pp. 11-12).

This last sentence raises a number of issues.

I. Why doesn't cognitivism fit the bill as a non-species-specific definition of cognition?  (Set aside worries about definitions, for the present.)  Cognitivists have regularly been interested the cognitive capacities of non-human animals, e.g. chimpanzee abilities with natural language, animal capacities for self-concepts, animal capacities for tool use. Cognitivism seems to offer a non-specifies-specific "definition" of cognition and, in fact, includes this as a part of its active research program.

II. Why doesn't cognitivism fit the bill as a non-bio-chauvinistic definition of cognition?  After all, many cognitivists think that it is possible to produce computers that think and presumably these could be computers that are not autonomous (i.e., not robots).

III. And, why isn't it that some forms of enactivism are bio-chauvinistic?  Consider the versions of enactivism that claim that "life = cognition".  (Cf. Di Paolo, 2009, p. 12).  Or what of versions for which being cognitive entails being alive.

Di Paolo, E. (2009). Extended life. Topoi, 28(1), 9-21.