As NJ5 pointed out already the XBox 360 doesn't use an Intel processor, but the loss of the GPU should have had a minimal impact because you access the GPU on the XBox 360 (and original XBox) through DirectX which has a hardware abstraction layer to enable you to switch hardware; it should be similar to switching your graphics card on your PC from a nVidia graphics card to a ATI graphics card.
The problem with both Microsoft and Sony was that backwards compatibility was never considered when they were designing their system and was worked in as an afterthought. Microsoft and Sony both decided to abandon their existing CPUs and go a completely different route with their current generation consoles but they didn't have to. Sony had to include the emotion engine in the PS3 because the Cell processor doesn't share a similar instruction set; and then later had to remove it because they couldn't afford it.
To put it another way ... Modern PCs are entirely backwards compatible with decades worth of previous systems mainly because it is the #1 consideration with PC hardware; they are dramatically more powerful than they were 5 years ago, and at the same time they are much more affordable than they used to be.
I'm not saying that their choices were either good or bad, but they could have easily designed a system which was powerful, affordable and maintained backwards compatibility. For Sony and Microsoft their decisions may have worked out for the better because Microsoft was "Screwed" by both Intel and nVidia in the last generation and (we assume) wanted to be able to own the processors in the XBox 360, and Sony always talked about how the Cell processor was going to become important to the entire company (including discussion of it being a DSP replacement); but Sony and Microsoft could have easily made different design decisions, and partnered with different companies to produce their systems in such a way that they were 100% backwards compatible.
