ARM and SAP are both Internet companies without question.

ARM wouldn't be relevant at all without the Internet. In practical terms its product is entirely linked to the Internet, specifically the mobile Internet.

ARM is not a website, sure, nor an app. It's as much an Internet company as AWS is. One could pretend AWS could exist in some formulation without the Internet, but that would be silly. The same is true with ARM as it exists today, the Internet made them what they are. If you remove the Internet, which neuters smartphones, ARM all but vanishes; thus, they're plainly an Internet company. You don't have to be strictly software to be an Internet company.

You could then call Nokia and Ericsson Internet companies, but they also existed for purely voice-based services. ARM chips go into all kinds of things like hard drives and microcontrollers that are not Internet based. Yes it's true that ARM has exploded due to cell phones, which in turn heavily rely on Internet-connectivity for their value proposition, but the Apple Newton used an ARM-chip well before 3G.

This article is talking about 'internet-vision'... I don't see how ARM fits into that vision, especially since it effectively predates it. Plus it's now been sold to Softbank at any rate.