With that said, estimating size of the cell and having a guess at it's weight should be possible from the document and video.
Not really to the accuracy needed, though. 400Wh/kg number is exactly what makes all these claims so outragerously significant. At 250Wh/kg, it would be just... meh.
But, a product performing similarly can already be bought off-the-shelf, if 200Wh/kg is acceptable. Without any real reference for measurements (not even a banana), volumetric energy density could be estimated to maybe 50% accuracy if even that, and gravimetric energy density not much at all.
From images you can of course estimate that it's not 20 or 50 Wh/kg or something like that. It's better than that, for sure.
Note that the round-trip energy efficiency at 11C is 82% (and 87% at 5C), which means it does not have miraculously low internal resistance. So if this was real, it would be most usable at 5C max and even then with thermal management, but of course even that is a remarkable number.
But the charge curve, the amount of internal resistance, all mean their sample could be just a state-of-the-art, COTS NCA/NMC high-power cell, overdriven to 4.3V and 11C rating, because in such test, they don't have to care about aging (because it's tested only for a few cycles, not 100000). Heck, 10 year ago I tested COTS LCO and NCA cells charged to 4.45V instead of rated 4.20V, seeing +20% capacity, and no damage / no capacity degradation after 10 cycles, after which I stopped. I could have had VTT to rerun the same test and claim that I have a new battery tech with 20% better capacity, and higher 4.45V voltage, definitely not based on lithium and cobalt, and capable of 100000 cycles. This kind of stunt is easy enough to arrange.
Then again, I'm not 100% sure if even the best COTS NCA/NMC cells behave exactly like this when abused at 11C. I have not personally tested. But they are pretty close, so a real possibility that's all that's going on.