Yeah, basically Intel's "in" to console gaming would have to come through another platform holder. Some crazy off-chance Sega, NEC, SNK etc. decided to re-join the fray. They certainly have a lot more going on than, say, Atari or Intellivision, and those two are trying their own new consoles, but I don't see how Sega or SNK could pull off a 10th-gen console without serious funding backed by another company. NEC I guess maybe could, they were pretty huge at the time of PC-Engine though I don't think they're as large anymore. But they probably have other reasons to not bother.
So it's either that or a new company emerges and tries their hand. It would still be a smaller type of thing likely not to compete directly with Sony/MS/Nintendo but...I can see a company like exa-Arcadia maybe trying a consolized version of their arcade system for the home, maybe they secure some sweet deal with Intel on the CPU/GPU front and use that in a next-generation exa-Arcadia arcade system and consolized "home-friendly" system (it doesn't have to be specifically targeting home users, just more an extension of letting arcade gamers play the games on a home-like console device featuring the same tech, with some way of keeping arcade operators in the loop for revenue and also providing a means of buying/renting such units, playing the games at home, etc.).
That's a future path for Intel into non-PC gaming spaces I think, just maybe don't expect Intel tech in a mainstream console suiting to take on the next PlayStation or Xbox (or Nintendo device, at least in terms of marketshare. It could easily beat Nintendo in specs, though).