This is a fun little problem that's remarkably close and the math is pretty easy when you use the right periods.
Venus' synodic period, relative to Earth, is 583.92 days on average. He uses 584, but lets strive for accuracy. Venus' solar day is 116.75 days, so 5 solar days is 583.75 days - Venus does 5 rotations in nearly the same amount of time that Earth and Venus line up together.
More details below:
Eccentricity in this case, doesn't matter, so, even though Earth will move different amounts in those 218 days past the first full year, it's the average that matters.
A cool property of tidal locking is that the locked objects can move ahead or behind and it doesn't undo the locking. For example, our Moon is tidally locked but its eccentricity still creates libration. Pluto can move ahead of or fall behind its 3/2 resonance with Neptune, but Neptune's gravity draws it back, so it never laps the 3/2 resonance. It stays locked. All we need is the average synodic period, or 583.92 days.
.03% is closer than many tidally locked objects' periods can be, but that doesn't mean they're tidally locked. One can still lap the other.
We know it's coincidence because orbital periods, which determine the 583.92 ratio, are highly stable and Venus' orbital period might change very slowly, but only very slowly.
The variation is a little under .03% or 3 parts in 10,000. It's close enough that we might want to get more decimal points to get more accuracy, but that's where I run into some problems. I can't find any more decimal points to Venus' solar day, just 116.75 days or 2802 hours. No mention of fractions of hours.
His numbers on the video looked wrong to me at first, but he uses sidereal year, not the more familiar tropical year. Most of us think of an Earth year as 365.2422 days, not 365.256 or 365.26 as he writes on his video. I don't think it makes a big difference which we use, tropical or sidereal years. That only changes the numbers slightly. Both still fall to about 3 parts in 10,000.
His numbers posted on the video:
Earth Orbit: 365.26 days*
Venus Orbit: 224.70 days
Earth/Venus closest: 584 days
Venus Sidereal day: 243.03 days
Venus Solar day: 116.75 days
Numbers I used
Footnote: @BMF posted a research paper that says Earth may have an effect on Venus' rotation speed - copied here. I'm going to leave my "it's coincidence" comments above, because it seems more likely to me that it's coincidence, but maybe I'm wrong.