This isn't true competition. This is vertical integration.

Amazon isn't offering to deliver Walmart packages for a price.

Actually that's exactly what the article is about. Amazon has already had their own delivery drivers for a long time, they are now directly competing with UPS and FedEx by shipping packages for businesses that don't operate on Amazon's eCommerce platform.

If Amazon loses money on each delivery to stoke its market share, Walmart should use it as its delivery service until Amazon has exhausted its foray into last mile logistics.

That's literally exactly what they're offering. This is directly competing with FedEx/UPS.

"...the new service will entail the online retail giant picking up packages from businesses and shipping them to consumers."""