This is not really surprising.
However ...
People might say anything to surveyors, especially when they think it's what they're "supposed" to say (rather than because it's what they actually believe)
[1]. For that reason alone, any poll or study based on self-reporting (like the one referenced in the OP) should always be regarded with a gimlet eye, no matter what results they might indicate.
And even when respondents really do (think they) agree with something in the abstract - when doing so is no more expensive to them than filling in some circles on a questionnaire, or the like - things might actually turn out to be quite different in the not-so-abstract-or-costless real world. IOW: "Talk is cheap. Whiskey costs money."
Then there's the rather important matter of what, exactly, is being denoted by the concepts of "offensive speech" and "death penalty".
What do the respondents understand "offensive speech" to mean? The concept of "offensive speech" could easily and reasonably be considered to include things such as "fighting words" (i.e., things which are allowed for as actionable threats under libertarian theory). On the other hand, it could be understood (and is, by some) to include things such as merely refusing to use someone else's "preferred pronouns" (i.e., things which are not allowed for as actionable threats under libertarian theory).
What about "death penalty" (or any other "such harsh punishment", as the proposition is stated in the OP). Do the respondents understand this to refer only to capital punishment as the end result of a structured and formalized trial process? Or do any of them understand it to include the more immediate (and rather less formal) consequences of saying the wrong thing to the wrong person at the wrong time in the wrong place? (If it is the latter, then our very own @
tod evans might well agree with the proposition as it is presented in the OP - and he is certainly no left-indoctrinated college-boy snowflake.)
Finally
[2] (and this is what really grinds my gears about things like this), notice how the wording of the proposition is engineered in such a way that it can be agreed to by both (1) careful-minded, precise, and dispassionately analytical respondents, and (2) ideologically doctrinaire respondents who endorse (threats of) violence in the cause of controlling speech and policing thoughts. Consider the first two sentences: "violence in response to offensive speech is not a new phenomenon" and "in some cultures, some types of offensive speech even merit the death penalty". Both of those statements are factual, and neither is an opinion over which people can reasonably disagree. They are used to set the context for the third statement, which is the proposition respondents are being asked to agree or disagree with: "some speech can be so offensive in certain cases that it merits such harsh punishment". Note the use of the word "merit" in both the second and third statements. In the second statement, it is used in a positive sense to convey the fact that "in some cultures" the "death penalty"
is applied as a punishment for "some types of offensive speech" (regardless of whether it ought to be). But in the third statement, it can be interpreted in either a positive sense (e.g., "such harsh punishment"
can be applied for "some [cases of offensive] speech", regardless of whether it ought to be) or a normative sense (e.g., "such harsh punishment"
ought to be applied for "some [cases of offensive] speech"). This is a slippery, weasel-word equivocation. The dispassionately analytical can agree with the survey proposition in a "legalistic" sense while rejecting it in a "moralistic" sense, while the ideologically doctrinaire can agree with it in both a "legalistic" and "moralistic" sense.
Furthermore, the equivocation is weighted in favor of the ideologically doctrinaire response by the moral relativism inherent in framing the proposition in terms of the fact that "some cultures" allow killing people for "offensive speech". But what have "some cultures" got to do with it? Why are they explicitly mentioned, but not the ones that
do not allow killing people for "offensive speech". What the hell does the fact that culture X allows killing people for "offensive speech" got to do with whether
our culture ought to do so? It is difficult to avoid the suspicion that the whole point of that reference to "some cultures" is an attempt to cow respondents into agreeing with the proposition in a normative, "moralistic" sense (out of fear of being accused of the terrible sin of judging "some cultures" to be morally inferior, or even just wrong about something).
[1] This is especially apt to be the case for college students (and faculty). Ironically, few places seem to be more stifled by groupthink, thought-policing, and the fear of consequences for saying the "wrong" thing than modern college campuses.
[2] TL;DR for this paragraph (I typed all that out before I saw ASoL's post, and dammit, I ain't gonna waste it

):