I'm not sure how that statement addresses the point made by GP, who said, "...their websites are often terrible on a laptop, which is how I use the Internet."
If not the de facto guidance of mobile-first design, the de jure guidance steers designers toward reduced functionality. The overwhelmingly common outcome of a mobile-first redesign of an application is dramatic reduction of functionality, often spun as a simplification. I would prefer if mobile-first redesigns retained existing functionality but I acknowledge functionality may be reached in new ways that better fit the capability of the device.
The problem is not that mobile-first design strips features only on small view ports; the problem is that mobile-first design strips features full-stop.
Again, your feature is what you can accomplish with whatever it is you're designing. If it's a database of information with tons of categories then it's an IA problem from the tightest box first and then using more space as it becomes available. If a user can't get to the same information on any device then the design ain't working. If its a piece of accounting software you'll have a bunch of crud operations happening and need to focus on designing great forms. I think most large companies basically decide to cram their mega menu into a side are menu, then expose the search bar and put their app in read only mode. Very much like slapping agile on your team to solve your efficiency problems, it won't work.
Another explanation: sometimes the device really is too small for the information. Mobile devices are terrible for a lot of things. People with laptop or desktop computers shouldn't pay a price for that. "Mobile first" is okay in some cases as long as it isn't "mobile on every device".