The primary thing that's missing is any evidence that the claim is true, or even plausible. There's no indication that they even tested this with kids.
I don't take advertising at face value, even if that advertising might appeal to sci-fi sensibilities. Your question has an air of "well you can't PROVE the flying spaghetti monster is false."
I think the plausibility is granted by the usage of the emotion intelligence model[1].
However, I agree with you that this is very thin ice. Given the selection of books used as decoration in the video, the authors seem to have more of a business background [2] than one of psychology.
I don't like calling someone a liar when no evidence is present (either way). I would rather say: 'Bold claims, can you prove it?'
Those books made good props for the demo but I should add that we aren't exactly experts in it either. I have a background in computer engineering and math at UIUC and my cofounder has a background in data science and machine learning from city university in london and architectural computation at UCL.
Ours are indeed bold claims and we have updated some copies on the website to update our core value prop