So how'd Sega release a mainstream console with a cross-shaped pad, something no one has done since the NES? Simple, they worked around the patent. If you recall from the article linked above, Nintendo's patent described a cross shaped key on a circular disc with a central fulcrum, like so:
Notice #13, it's the fulcrum on the bottom of the disc.
Now, let's have a look at Sega's solution. At first glance, it looks like many other d-pads. No circular base obviously, but the differences don't end there. The right side is keyed, so it can only go in the controller one way, which is kind of unusual but not unique. This is important for the Dreamcast though 'cause, if you look closely, the right side is also slightly taller than the left. It had to be, 'cause the DC pad was taller in the middle too. If the d-pad was flat, it would appear to sink further into the pad on the right side.
But here's the biggest reason it doesn't infringe on Nintendo's patent: it has no fulcrum of its own, the round dome is part of the rubber membrane:
This critical difference keeps the lawyers at bay, 'cause it no longer, in several significant ways, infringes.
A lot of people complained about the DC pad when it came out, but I reckon they're just whiners 'cause it never really bothered me. It's certainly more accurate than many, and despite its height, not much more wobbly than a Saturn pad (which is widely accepted to be the best pad ever).
A reader asked about the plastic parts grinding on each other, wondering if the resultant dust was a problem like it was for the Neo CD pad. The short answer is no, it's not a problem, but yes, there's some dust created. Plastic parts grinding on each other is bound to do it. My old dreamcast pad had barely any inside it, but no doubt a heavily used pad will have more.
Still, the tiny surface area, hard plastics used and the minimal movement amount mean that very little damage is cause by this wear. And because it's two spheres, the result of any wear is a pad that sits a little bit lower, which is hardly a problem.