So to answer your question, I wouldn't quite agree with the professor that from a modern perspective, the Republicans formed to oppose a "rising" planter class--but that's because in retrospect we can see that the planter class wasn't so much "rising" as "arisen" already--and they were reaching their limits and they knew it. But it would be quite reasonable to say that the party emerged in response to a perception that the planter class was not done rising yet.
It is a gross caricature to reduce the entire secessionist movement, let alone the South as a whole, to just some monolithic "planter class." But on the level of gross caricatures, which are a major factor in political thinking after all, the "planter class" is indeed about as iconic an image of the North/South divide as one could have. They certainly were the leaders of southern society; that society certainly did align itself with their values and interests, and what the secessionists ultimately demonstrated in the Confederate constitution and the actions of that government and its constituent secessionist states was precisely the sort of threat that a large variety of Northerners unified against in the Republican party.
In order for the "planter class," and a wider range of interests associated with them, to survive on the terms they were accustomed to, let alone expand, they perceived a need to force the larger Union to accommodate their interests on an ever-expanding scale. This had been going on for generations before the Republican party formed and I think the Republicans were correct to believe they would need to organize and make a stand to stop it. I might quibble with the idea that the constellation of pro-slavery interests were "expanding" if this implies the notion that they suddenly started doing so out of a blue sky; they had expanded quite a lot, and strongly influenced Union policy as a whole in doing so. When I say that they were reaching the end of their rope, I assume in saying it that the northern and western interests increasingly exasperated by the imperatives of the slave-owning section of the nation would of course make such a stand. If they unaccountably failed to do so, well then I guess the slave power would indeed have continued to expand.
So--considering that one job professors have is to disseminate knowledge and provoke thought broadly, in a sound-bite age such as ours, I certainly forgive her for using such a simplistic image. On the level of simplistic, sound-bite, bumper-sticker images it is true enough. One hopes that people drawn into the discussion would learn or bring with them more nuanced information and detail.
I also realize she isn't putting this out in a vacuum. The past century and a half is full of all sorts of apologetic balderdash meant to obscure the reality of what was happening in the mid-19th century USA. Some counter-memes are in order.
In championing the Republican Party of the 1850s and '60s I hardly mean to suggest this has much bearing on what that party has come to stand for nowadays.