The explanation is needlessly long-winded, and she should have calculated (30x2) before (10x5) to remain consistent with later algebraic formalism the students will learn, but this is just classic FOIL, and absolutely the standard for multiplying two-digit and larger numbers.
(Computation using an abacus or soroban encodes the same method, which is where algebra got it.)
My daughter (7 this month) is a (new) 2nd grader in the USA, and a 1st grader in Japan (the two academic years are out of phase); she attends a private K-12 school, a Japanese school on Saturdays, and spends summers in Japan, where she attends a soroban academy.
She knows how to multiply; she sort of “figured it out” last year, but has started learning it formally as a side product of learning to use a soroban; her school is also mixed-age, so she’s in class with 3rd graders (who certainly learn to multiply), which probably advances her.
Her school in the USA uses “Everyday Mathematics” (not my favorite; I’d prefer Singapore), and in Japanese school she learns their geometric method of multiplication (counting intersecting lines), while in learning the soroban she applies FOIL. In the Japanese curriculum, tables through 9x9 are learned by rote, since you need quick command of that to apply the FOIL method.
She has a pretty good “sense” of numbers and their combinations already, and also delves into negative numbers, properties of some numbers (such as pi), the notion of infinity, set properties, and geometry (I will say kids learn basic geometry, like polygon classification, earlier now than I did as a kid.) That’s all stuff she learned in 1st grade in the USA.
I have raised her “zero digital”, so she has never been permitted use of calculators, pads, etc; none of her schools rely on such tools, either. She does use a soroban (mostly for fun), but as an analog device it helps to understand the math operations she uses.
I’ll probably buy her a slide rule someday
And we work math into our daily lives, playing games (she’s now a ranked chess player who reliably beats ME; humbling!), measuring things, and so on. We’re very “outdoorsy”, and take two ten-day camping trips per year (frontier style, with tents and no electricity), and we always wind up working some impromptu engineering in, rigging stuff with paracord and the like; last Spring she went on her first wild caving trip, and we did a LIDAR survey with her helping map the cave.
(Yes, this comes off as a lot of humblebrag, but I mention it to emphasize that even if you have access to great schools, if you want your kid to be Good at Math, that happens as home, not in some STEM or STEAM program.)
I’m also a physicist, so I obviously model “using math in daily life” quite a bit.
tl;dr: The video depicts a pretty good way to understand products of two-digit numbers, though it could use some finesse; good pedagogy, iffy presentation.