I think the implication is it should also apply to sales within their brick and mortar shops too, otherwise it's a bit hypocritical. It would also create a disincentive to use online sales channels, which could create knock on negative economic effects.

The bigger question is whether this would affect in-store (vs online) house brands.

If the rule only affected online house brands, it would tilt the field in favor of Walmart, Costco, and Kroger, who could all continue selling their house brands in stores. For e.g. Kroger, where online sales are a tiny percentage, this would essentially represent a carve-out.

Looked at another way, this could be seen as a tax on people with mobility challenges. (Because no house brands on the delivery services => higher costs.)