This has to beth weirdest start to a thread ever. OP posts a question whis clearly going to get a lot of 'YMMV' answers. Then gets four positive responses, two negative ones, two post about physics but 7 'YMMV but if it's fun, go for it' responses - complains about negative and physics posts despite them being in the minority.
I am just curious, why post this at all if you are going to make that response to the posts that went up? To prove a point? To try to gather evidence to show a dm who already said no? SOme kind of weird plug for Guardian Of Order?
In answer to the question - No, with caveat. If this was one of my supers games then yes. Hell yes. My supers games are all about cool stuff like this. If this was a D&D game based on the western genre or manga or martial arts, maybe. If it's straight fantasy, probably not. It's about suspension of disbelief for my players. If one week someone damages someone with a playing card, next week my players are going to try paper cut damage, or start collecting all the cards they come across rather than buying weapons. Because I have set a standard that my universe works on some kind of physical laws. BUT - that's just me. Maybe if you were trained in card fighting as part of the backstory, that'd be pretty cool. I would of course then include a card golem that was razor sharp.
As for the video. The mythbusters are at best like baseline scholars. 1d4+dex damage could probably kill them. Definately two hits. That guy taking the cards to the chest. Nowhere near death. That's the kind of damage I hand out when someone makes a saving throw and takes no actual HP loss.