The CNN Poll was not only of southern whites
The CNN poll of people who watched the debate was a little bit republican-heavy, meaning the audience for the debate was a bit republican heavy. It was also a more partisan audience in general, as one would expect. (Fewer independents than the national average.)
The poll was about half the usual sample size for a national poll (I think it was 430 people) which makes the margins of error wider.
So it is far from a great poll.
Unfortunately, however, some folks made a bad reading of the cross-tabs because they are not used to cross-tabs from a 430 person national sample, and concluded that the poll only included middle-aged and elderly southern whites.
That is incorrect. The many "N/A" indications in the cross tabs indicate subsets where the sample size would make the margin of error so large (over 8%, 9%) as to make the datum not worth reporting as an individual result. That is a normal practice in reporting these things... when the MOE is bigger than the sample it starts getting silly. And with a sample of only 430 most sub-sets will have huge margins of error.
In a typical national poll the sample size will be 800-1200 people so if you set a MOE threshold for subset data of 8% MOE or 9% MOE most categories will have a large enough sample to be under that cut-off. In a sample of 430 voters, however, a lot of sub-categories will fall into that N/A range.
There's nothing wrong with the CNN poll as what it is, which is a poll of people who watched a particular TV show. People who chose to watch a debate are not a random sample. Republicans have had a 10% edge in "very interested in the election" all year so it makes sense the viewing audience was a little disproportionately republican.
I loathe CNN, but the poll is not glaringly bad as a poll of reaction by the audience of the debate. Any "flash poll" is going to be below usual polling standards, including this one.