Just to add to the preponderance of circumstances for Ellen to win, we have just had eight years of Gary Hart. And he's not out of office just yet. This show has the option to drop Hart and Clinton scandals at the same time, if it wants to.
It does seem unlikely that a woman like Ellen would win the GOP nomination in OTL 1992. We've heard exactly one extremely vague insinuation that she doesn't support working families to the degree that Clinton does. We know she's on board with stem cells. I have to once again assume that the left wing of the GOP has been shored up ITTL. At least enough to win FPTP primary contests against conservatives. The fact that both Dole and Buchanan were mentioned as being in the primaries may have split the conservative vote, but you'd still need a good base of moderates to fight against the stigma of being a "maverick" lady Republican in 1992.
One thing that might have happened: a Silicon Valley more aligned with the GOP than IOTL. A more technocratic GOP, capable of embracing some of the weird "radical centrist" dogma you often get drifting out of NoCal. Still very pro-business, pro- "disruption," but also pro investment in STEM and a meritocratic view of social advancement. The government can intervene to level the playing field to allow the great-but-disadvantaged to excel, but don't do it on moral principal.
Another head-scratcher is that somehow Gore is Hart's vice president. If he's been the VP since 1984, he would've been about 36 at election time and IOTL would've been still in the House (he won his first term in the senate in '84). We know Howard Baker's in the senate going into '84 thanks to season 2, so the best he could've done was somehow replace Sasser in '82 (he'd be too young to meet age requirements to run in '76). Or they plucked him out of the House and put him on the Hart ticket. Not likely. Hart's only in his 40s; he wants someone older, and someone who represents a different wing of the party (basically the Ellen/Larry conversation from last episode).
The other possibility is for some reason Hart needed a new running mate in '88. That's still a little off from what's presented, as Gore would absolutely clear the field in '92. No way Clinton runs with all the Third Way peeps lined up behind Gore. Hart would totally try it: extend the Third Way momentum beyond his presidency, absolutely. The question is, who was his VP in '84, if this is the case?