Science isn't a living person. If anything they mean “scientists say”, and even scientists more often than not will not say things. A scientist is a person who tests falsifiable hypotheses in experiments that adhere to the scientific method. These experiments will lead to observations, and these observations are basically data. Data, even less so than scientists, will definitely not say things, and it definitely does not mean things. Data is not causality, and it rarely is correlation. It takes knowledge and context and understanding of a field to properly assess that data to draw conclusions. Rarely does the data speak for itself. “Science” in this context is misused by people who do not understand the science to appeal to authority. Especially younger, impressionable demographics are vulnerable to “science”, because in an unreflected mind “science” is the one and only¹⁾ and when science says so then it must be true, even if science never said anything.

More often than not, the “conclusions” drawn from presented studies or general research papers are a little bit more… enthusiastic than what the paper actually suggests. In the case of the DEFCON video “DEFCON scares me an science says it will scare you too” the premise is that “science” found something inherently and uniquely “scary” in DEFCON that affects everyone equally. Depending on how you want to see it, either you accept that the concept of fucking dying is perhaps a little bit disconcerting to humans (which is not new or something that needed science to verify) OR you say that there is no one such thing that every human ever will definitely always respond to with fear (ie. getting scared), but either way you will have to agree that this is NOT what the study said. The relevant study here is named “Education from inside the bunker: Examining the effect of Defcon, a nuclear warfare simulation game, on nuclear attitudes and critical reflection.”²⁾ and, as is already apparent, does not actually study emotional response to the video game DEFCON and instead examined how, in people, the perception of “nuclear attitudes” changed after playing DEFCON. TL;DR: Most people after playing DEFCON took the threat of nuclear war more seriously than before playing DEFCON, in comparison to those who did not play it.
The science does not necessarily contradict the claim of the video title, but it's clear that the science, apart from not saying much at all, definitely did NOT say what the designer of the video wanted it to say.
In its most fundamental sense, “Science says” is often used fallaciously by taking studies, finding in them data that points in some direction, and then going on to claim that study has established “facts” in that direction even though the science has, if anything, only ever pointed in that direction. It makes for some good headlines, though.

“Science says”, while perhaps semantically inaccurate, wouldn't even be necessarily deceptive: Science “says” that climate change exists, science “says” that the planet is older than 5000 years. Really it's about presentation: An actual scientific study wouldn't label itself as “hello I am a scientific authority”, it wouldn't invoke the entire body of “science” as their foundation for an argument, it wouldn't make these vast, emotional claims. This is how “Science says” is mostly found in outlets that more often than not do not know what they are talking about. It's clickbait.

Remember that science is done by doing science, not by wildly claiming that something “is” science and therefore good or correct. The amount of scientific theory that is being peer reviewed and/or ultimately falsified is immense, so don't rely on saying that something is science. If one doesn't know more than “well, it's a scientific fact” or “but it's science” then odds are they shouldn't speak at all, they probably have very little to contribute.