There are many ranked voting systems and that one is called a "Borda count." It's really cool but it has its own flaws, as you'd expect from Arrow's impossibility theorem.

Here's the most basic problem: the video that we're looking at made an implicit assumption when it proposed ranked voting: it said that "here are peoples' preferences!" and then it copied those preferences over to the ballots. Given the way that they're doing ranked voting, this equivocation makes sense, of course you're going to rank in your actual preference order. But with the Borda count this assumption is totally wrong and a lot of the confusion from first-past-the-post systems reoccurs: there is no reason to vote your actual preferences. Consider the 2016 US presidential election as done via Borda count, if we assume peoples' present polling is honest. Think about someone who supports Jill Stein; their preferences are typically Jill > Hillary > Gary > Donald. Will Jill lead their ticket? Given the very lackluster showing of Jill, they will probably narrow down the race mentally to "Hillary or Donald" and turn in the ballot "Hillary > Jill > Gary > Donald," to try to avoid a Trump presidency. It's the same spoiler effect as we had before.

It's not just an isolated problem like that suggests. Suppose an election where we have three candidates, Alice, Bob, and Carol. There are nine voters with the preferences,

    4xABC, Alice > Bob > Carol
    1xACB, Alice > Carol > Bob
    2xBAC, Bob > Alice > Carol
    2xCBA, Carol > Bob > Alice.

Alice is the majority's first choice and only 2/9 of the peoples' last choice, so you'd figure she'd be a shoe-in to win the election. Indeed, she'd win a ranked-runoff election and first-past-the-post election, while the pairwise election has the following ballot counts:

    A beats B 5 - 4
    A beats C 7 - 2
    B beats C 6 - 3

The pairwise election therefore also decides Alice > Bob > Carol. But while these other systems all have Alice winning for relatively easy-to-understand reasons, if Alice's supporters turn in honest ballots in the Borda election, then under a Borda election, Alice LOSES!

This is because the remaining four voters see it as down to an Alice-vs-Bob election and want Bob to win, so they turn in ballots saying BCA. The resulting total of points (3 for first place, 2 for second, 1 for third) is:

    (ballots: 4x ABC, 1x ACB, 4x BCA)
    Alice: 4 * 3  +  1 * 3  +  4 * 1 = 19 points
    Bob:   4 * 2  +  1 * 1  +  4 * 3 = 21 points
    Carol: 4 * 1  +  1 * 2  +  4 * 2 = 14 points

Alice however is a savvy politician and convinces her own supporters to rally against Bob to get Carol to look much better than Bob, so that they hand in ACB ballots. This is a measured tactic to turn it into an Alice-vs-Carol race which gets the BAC voters back on her side, since now Bob is no longer a strong contender and they vote Alice. It gets complicated!

    (ballots: 5x ACB, 2x ABC, 2x CBA)
    Alice: 5 * 3  +  2 * 3  +  2 * 1 = 23 points
    Bob:   5 * 1  +  2 * 2  +  2 * 2 = 13 points
    Carol: 5 * 2  +  2 * 1  +  2 * 3 = 18 points

Except Carol has a trick up her sleeve. She sees that Alice is doing this and so runs with her friends Dwayne and Erica, who agree with her on everything but are slightly less preferred by the voters in general. Since they are so similar our original setup is 4xABCDE, 1xACDEB, 2xBACDE, 2xCDEBA. Now if the ballots are cast with the smear campaign against Bob in full force you have:

    (ballots: 5x ACDEB, 2x ABCDE, 2x CDEBA)
    Alice:  5 * 5  +  2 * 5  +  2 * 1 = 37 points
    Bob:    5 * 1  +  2 * 4  +  2 * 2 = 17 points
    Carol:  5 * 4  +  2 * 3  +  2 * 5 = 42 points
    Dwayne: 5 * 3  +  2 * 2  +  2 * 4 = 27 points
    Erica:  5 * 2  +  2 * 1  +  2 * 3 = 18 points

Suddenly Carol wins! Or, if Alice smears Carol almost as much as she's smeared Bob, then Dwayne just takes Carol's place and Dwayne wins; remember, they're largely identical! (You might wonder whether the effect of adding Dwayne and Erica to the voting has meant that Alice doesn't need to smear Bob anymore and whether Carol becomes her enemy #1; the answer is that if we just substitute C -> CDE in the above "Bob wins" tally then Bob gets 34, Carol gets 32, and Alice gets 29, at which point we need to re-evaluate the strategic voting because you KNOW that after that mock-poll comes out, the news will classify Alice as a 3rd-place finisher and her own majority voting block might rebalance around the assumption that it's largely a Bob-vs-Carol race.)