No, "means" is correct — although the sentence is poorly written on the whole, and especially poorly punctuated around that area. I assume it's transcribed from oral conversation.*
There are a few different senses of the word "mean". Here are three relevant ones.
To mean [definition]. e.g. "Isolate means cause to be alone." In this case the subject must be a word, a term, or a phrase.
To mean [consequence]. e.g. "The litmus paper turning red means the solution is acidic." In this case the subject is some fact or action or cause.
To mean [intended message]. e.g. "Hadn't you better lay off the chocolates?" — "What do you mean?" — "I mean you've put on a lot of weight over the holiday." This is the broadest one, and while the subject can be a person, it could also be a book or a song, for instance.
There are more, but that's enough to look at this sentence.
First of all, it's clear that "they share half of their genetic material" is either (1) or (2). The identical twins are not trying to convey a message (3) — they haven't said anything and are not agents here at all. The phrase is given either as a definition of "identical twins" (1) or as an explanation of the relevance for the study (2).
Once we understand this, we see that the only plural subject, "twins", is ruled out. The real subject is either "the term identical twins" or "the fact that they're identical twins".
This kind of implicit subject is extremely common and expected. However, the wording and punctuation of the sentence do not help you to parse it correctly. Here's a better wording for (2):
...they've done various studies of identical twins — which means they share half of their genetic material with each other — and it turns out...
And here's a better wording for (1):
...they've done various studies of identical twins (people who share half of their genetic material with each other), and it turns out...
* In the original oral conversation, I would expect a pause after "identical twins". The speaker then looks at the interviewer, or at the audience, and, raising their eyebrows or index finger meaningfully, adds the parenthetical "That means they share half of their genetic material" and then resumes; this would be meaning (2).