On the definition of 2-rigs

Question

I am reading the nLab entry on 2-rigs. In its list of definitions, it says that a 2-rig category can be defined as a $Ab$-enriched category which is enriched monoidal. Why is the enrichment in $Ab$? Wouldn't it be more natural to enrich it on commutative monoids instead of abelian groups? Doesn't this contradict the fact that we are defining 2-rigs instead of 2-riNgs?