Why would you even begin to think that's the case?
The Star League's dominion over the sphere was a thing that explicitly involved the houses. I see no reason that a third league under the leadership of a clan should require their extermination.
Well there's outright extermination, and there's disenfranchisement. What I worry about isn't so much the former as the latter.
But why would I think what I think?
1. There is indeed clarification that the ilClan will actually BE Clan. I know, there was always slim chances the Republic would defeat the Wolves and take the title of ilClan for itself to dictate to the Clans how they'd behave from now on. Now that's gone from slim to none, which is a minor shift but it's not insignificant.
2. Based on the language intended for the ilKhan's eyes, the ilClan appears to still consider itself separate from and superior to the native Sphereoids. That would make a Dominion-like hybrid rather implausible for the ilClan.
3. Going back to the bolded text in the quote, the IS has gone thru "enormous change". If it were just the Republic falling to Clan control, that wouldn't rise to the level of "enormous change". And I find it unlikely that the 5 Houses simply going through a hundred years of "PeaceTech" with the ilClan would count as "enormous change" either.
4. The ilClan controls the Inner Sphere to the point that it apparently controls who gets to climb into a cockpit of a mech. And uses that power to leverage native populations to vent their grudges against each other.
5. Mechs looking like mechs from the past provides a bridge of familiarity for the native sphereoids to the period prior to the ilClandom. This reiterates point 3 and enhances it. Things in 3250 are so unlike 3150 or 3050 that the ilClan is broadcasting mech fights explicitly in part to tickle the sheeples' memberberries.
6. We saw a Great House name called out in the cited Gunslinger. We don't know what a Gunslinger means in the context of the ilClan, but my gut tells me that if the Great Houses still exist at all, they exist because the ilClan
lets them exist. From a pride standpoint, that's little better than not existing at all. From a meta plotline perspective, if the ilClan achieved complete to near-as-may-as-well-be-complete control of the Inner Sphere, it'd be very sloppy to "resurrect" the Houses as viable opponents for the ilClan in a post "PeaceTech" setting. You'd require all new opponents for the ilClan to fight, and by that point I'm completely off the BattleTech train.