Saving this shit from 404ing.
I think the easiest way to approach this is if the major competitors to Sega/Nintendo simply never came into the market, and this is immediately important. The Sega Saturn ended up being rushed in the west in order to better compete with the Playstation, which ended up backfiring miserably. Had the Playstation never released, the Saturn would have most likely done better in the console market, perhaps keeping up with Nintendo. It's also worth noting that in the mid-90s, there were some that speculated that Sega would end up becoming bigger than Nintendo. For sake of argument, let's presume that Sega continued releasing consoles to this day, since that's a part of this hypothetical situation.
As Nintendo was, and still is, more focused on gimmicks, and Sega was more focused on technicals, odds are Nintendo would be relatively similar to how they are today, whereas Sega would be not too far off from what the PS4/XBONE currently are.
Speaking of the XBONE, the absence of the XBox line impacts the industry too. Halo would help popularize the current standard control scheme of shooters, and perhaps to a lesser extent, the popularity of console FPS games as a whole. Without them in the market, odds are the PC would still hold the lion's share of shooters.
RPGs would probably largely shift to Sega's control, due to the hardware limitations that started to show themselves in the N64 era. They'd make somewhat of a comeback in the Gamecube era as they did in this timeline, but still be a minority.
The handheld market would be very similar to today's market, with Nintendo duking it out with mobile systems, with Sega being an afterthought at best.
As to whether or not it would be as jewey, Nintendo would probably be in a similar boat as they are now. Amiibos would still be rampant, and they'd probably still be cracking down on fangames. Sega is much more difficult to say. Much of their positive PR has come off of the backs of the negative PR other companies have been receiving, the most notable recent example being Sonic Mania's existence. So whether or not they'd retain this or take a route more similar to the other consoles of today is up for grabs, as far as I know.