The gif of the knot does not show the set up, which is kind of unfair to the standard knot since that part is fundamentally baked-in to the standard knot. I'd love to see a video of the creator doing this from the start, because he probably is pretty good at the set-up which is just as important.
I think part of the reason why I don't find this faster is because I use the more modern style of flat/ovaloid shoelaces. Round shoelaces don't really get "twisted", and linen shoelaces are pliable enough for it to not matter, which means you could roll the laces around in your hand to get them to the starting position for Ian's knot. With the laces in basketball/running shoes, I think you need a bit more dexterity to manipulate the laces to get them to the point where they are 'flat' than could be managed with Ian's knot.
I don't think switching to Ian's knot and round laces would save me much time overall; the reason I like flat athletic laces is because I never have issues with the knot coming undone, loosening, or stretching/tightening. I use round laces on my work boots because flat laces are hard to untie if they get gritty, and I always have to double-knot them or they come undone. Since this is identical to the standard knot, I'm sure that would continue to be a problem, and I think the set-up for the standard knot makes double-knotting easier as well.
As a final note, my best friend ties his dress shoes this way (with the really narrow laces), and it is definitely faster all things equal. I think those narrow laces are probably the best use for this method.
All that being said, I originally found this site while looking for lacing methods, and it's one of my favorite sites on the internet. It's basically everything of what I loved about the "geocities" era of the internet (without the stuff I hated).
I've switched to using Ian's knot, and have found it to be both faster to tie and easier to set up. I think once you work out how to 'pick up' the laces in the right way, so that they are already in the correct starting position, it gets a lot faster/simpler to think about.
Of course, I haven't been in your shoes - my laces are all the round type and I haven't tried it with flat ones.
To each their own!
I feel it's a bit faster to do than my previous knot, however the real benefits are (for me) this knot stays tight all day long, and the tension is symmetrical (the knot doesn't slide on the side during the day, you never end up with one end longer than the other, etc)
The oval style with the sharp edges has a lot of the benefits of the flat style, but is more universally compatible. The flat ones don't always move well in round eyelets, they work better with loops in my experience.
The completely flat style doesn't tie well if one of the laces is twisted though. I think it's a great option for athletic shoes though, where you are more likely to care about a particular level of give, etc, and when you don't want your shoes to become untied. The round style is cheaper, and if you don't notice the difference it's probably a more versatile shoelace.
Plus you can do fancy knots with the round style.