Intel needs to be viewed as several businesses, one of which is their discrete CPU business, another being their flash memory, yet another being the McAfee software acquisition, and yet another something called the foundry business.
Foundry refers to having a business where you are simply the manufacturer of chips for other companies for their specific purpose without selling into the end market. These other companies contract to Intel to be able to build anything from a network chip to a graphics chip to a microcontroller or virtually anything else (besides memory), either as a standard product off-the-shelf, or as an application-specific integrated circuit. In order for Intel to make that happen, they need to provide the know-how to these manufacturers of chips either directly or through providers of chip intellectual property. This includes logic libraries (standard cells, hence my name), memory cells and compilers for SRAMs, analog I/O cells, mixed-signal like ADCs and DACs, PLLs, non-volatile storage, design rule decks for the process rules, and a few other things that constitute the building blocks of any chip.
Other foundries such as TSMC, Global Foundries, etc. have the same model, though Intel's foundry manufactures more of their own CPU (and other) products than for other folks. Intel decided to farm out some of that capacity to third parties and make additional money on any spare capacity they might have, particularly with their leadership in logic processes over other rivals in the discrete CPU business. One of the key aforementioned building blocks is the IP offered by ARM for CPUs, GPUs and bus interconnect. This ARM IP needs to be validated to work in their silicon process, and this is the essence of the deal - Intel's foundry customers would not do business with Intel without basic blocks like the CPU since ARM is essentially the most important embedded CPU architecture in chip design currently.
The way the summary comes out makes it sound like Intel is manufacturing chips for its competitor, but it isn't necessarily so since the Intel microarchitecture is very highly vertically integrated as a business with their discrete CPU division whereas ARM itself is just a provider of IP with their microarchitecture. Yes, in theory Intel foundry customers could be making chips to compete in some segments of the Intel discrete CPU business, but that business is still largely dominated in the server and desktop markets by Intel and its associated software ecosystem. In the same way, ARM dominates the handheld device markets where Intel has had very little comparative presence.
I can guarantee that Mr. Krzanich and the Intel board would never allow their foundry business to cannibalize their current core discrete CPU business for a "competitor" if they felt it was detrimental to their overall financial and operating picture. This ARM deal is a piece of a larger plan of maximizing their ROI on their very very expensive chip fabs in a market where they have typically had a lead in logic process technology at least one node ahead of their competitors historically. That advantage can be very important in mobile due to the cost and power savings vertical transistor process nodes now offer along with superior manufacturing capabilities as the scale of their other businesses has long demonstrated.