As people said in the comments, there is no distinction in a standard accent between the eccentricity of a person and the eccentricity of a conic section: /ks/ is used for both senses of the word.
However, it's not unheard of for people to "mispronounce" words written with "cc" with /s/ instead of /ks/. (Quotation marks because once a pronunciation becomes common enough, it's entirely a matter of opinion whether it should be considered a "mispronunciation". I have my own opinions, but I'm not interested in getting into arguments about that topic.)
In eccentric(ity), /s/ is not generally considered standard, in the sense that dictionaries do not list it, and pronunciation coaches and so on would not advise it. It may be possible to find some prescriptivist complaining about it—I will search.
non-standard [s] instead of [ks] in "cc" words in general
I thought I'd just list some examples of the general tendency I mentioned in the second paragraph above.
Here is a question posted by someone who says "asselerate" and "eesentric": Pronunciation of a double C. A comment by Erik Kowal there points out that some people apparently have /s/ instead of /ks/ in succinct, which is confirmed by Merriam-Webster.
More examples of nonstandard pronuncation of "cc" as /s/ are mentioned in the following Straight Dope Message Board thread: How do you pronounce these three very common words? (the words are successful, acceleration, and eccentric; the OP says "not sure about that last one but the first two are definite[ly]" pronounced with /s/ instead of /ks/ by two white male coworkers from Michigan). Other words mentioned in that thread: flaccid (much more established with /s/ than any of the other words listed here), accessory
non-standard [s] instead of [ks] in "eccentric(ity)" in particular
That Youtube video is a very interesting find! As John Lawler says, people often simplify consonant clusters in certain ways in fast speech. But that doesn't quite seem to be all that's going on in your example, because the speaker doesn't use a reduced vowel in the first syllable: actually, he uses a more emphatic-sounding pronunciation with initial /iː/, /iːsəntrɪsɪti/! To me, that indicates that he really doesn't think of the word as having a consonant cluster here at all (compare the use of /iː/ in the first syllable of words like essential or effective, or /oʊ/ in the first syllable of words like offensive). One of the Straight Dope respondents gave "ee-sen-trik", which has /iː/ like in the video, while another transcribed "S-sentric", which I would interpret as starting with /ɛs/, and a third couldn't decide between /ɪs/ and /ɛs/.
Actually, this reanalysis is something that I can attest that I had as a child (I actually thought of eccentric as having just /s/; I didn't just slur a pronunciation with /ks/), but I use /ks/ presently, and I always assumed my earlier conception of this word as having just /s/ was a kind of spelling pronunciation based on not mentally processing the fact that the "c" is written double. (Like how some people read misled as "missle'd" /ˈmɪsəld/ rather than /mɪsˈlɛd/.) But perhaps I had some aural exposure to this variant also.
The innovative /s/-pronunciation of this and other "cc" words seems like it might be based in part on the much more established pronunciation of flaccid without /k/. (Or, they might have just developed for similar reasons.) I personally have a hangup about consistency in pronunciation, so when I figured out I "should" be pronouncing a /k/ in eccentric(ity), I also switched to pronouncing it in flaccid. But my pronunciation here is pretty weird and pedantic; many people have flaccid as basically the only word where "cc" is pronounced /s/.
It's possible that some people distinguish between /ks/ in eccentric(ity) when talking about a person and /s/ when talking about mathematics, but I don't see any direct evidence of this from your videos. The nonstandard pronunciation I used earlier in life wasn't specifically for eccentric as a mathematical term, but for it in all contexts.