"We will solve your problems for piles and piles of money. Usually not problems that require technical breakthroughs or research level computer science knowledge, but ill-defined problems that involve many stakeholders, much politics, and complex business logic."
They make their money as a professional services company (a model Buffett has no trouble understanding) that uses technology.
That, at least, would be my take on it.
I think the business model outlined above is correct in the global strategy sense, even if you looking at a few pie graphs makes you think otherwise.
If they are tech-agnostic then they aren't in the hardware/software business, which was my original point. They are in the hardware/software business because it helps them take your money for the wetware side.
Like any lab looking at fundamental science, it's hard to judge how much of that activity leads to profit. Some research groups do also make/sell products that are cutting edge, though, on a consulting basis. E.g. the storage group in Almaden makes insanely large custom storage systems for very big - often federal govt - clients.
They're not just a plain boring services company.
I'm sure that quite a lot of research went into Watson, and I think IBM is betting big on that technology. Potential applications are in healthcare (to quickly find an answer in all medical knowledge), legal documents analysis, and so on.
They definitely spent much more on "ads during football games with the blue bars" in any given year than they did on the whole Watson project.