The video you posted is so full of strawmen that nary a crow will ever touch it, but I'm going to be the little crow that could. Let's do this point by point again. This time, their claims will be indicated with (C) and my refutations with (R).
C1: Libertarian Socialism involves state intervention to redistribute personal property (car, house, etc).
R1: Nope. The existence of worker co-ops, trade unions, or other forms of worker collectives alone as a dominant mode of production does not put a gun to the state's head and tell it to take your boat. What it does do is put a check on the power of the upper ranks in a business to endlessly unilaterally raise their compensation packages (thereby redistributing wealth from you to them and taking your potential future personal property away) since the workers would have to approve the pay grades. Research into actual worker co-ops shows that those at the top make about 20 times more than the lowest paid worker.
Part of the problem here in the vid is cherry-picking definitions for "libertarianism" and "socialism" and then asserting that "libertarian socialism" is logically impossible and inherently contradictory. If a system or thing exists and is distinct from other things, then it is so, regardless of logical contradictions that arise from our limited abilty to define it.
C2: You cannot have both a state with no control over property rights and "no state."
R2: Correct, that's not what it is about though, I'll start picking the straw out of my teeth.
C3: Libertarian socialism does not respect property rights. Capitalism does. (political compass meme)
R3: False. Libertarian socialism respects "personal" property rights (your car and your home) and your right to keep the full value of what your labor produces (though some of it is loaned to the business until you withdraw your share in the business). It does not, however, respect your right to lay claim over the value that another individual has produced with their labor just because you are not a tax collector and happen to own a monocle and top hat.
C4: Free things aren't free (student debt), someone has to pay for it, and it is implied here that it will be the taxpayers doing this.
R4: Firstly, quoting Chomsky's opinion on Mexican colleges has nothing to do with Libertarian Socialism. A libertarian socialist can like a policy that is not libertarian socialist for pragmatic reasons to benefit individuals who live under the current paradigm. A conservative could like a lifted restriction on bump stocks even if their full stance on guns is that they should be completely unrestricted. My brain hurts from this person's lack of proper analysis and incessant use of logical fallacies. Secondly, again, as I have said elsewhere, the students (assuming that they graduate and get jobs and work for a sufficient enough time) WILL be part of the taxpayer pool who pays for their education. It will still end up functionally being a loan, but just one that does not involve a private and unnecessary middle man, and where risk is more evenly distributed. I welcome your dispute on this point.
C5: Socialism requires a strong state to get off the ground.
R5: Strong in what way? Having a set of laws and enforcers? Capitalism needs this as well. Whose gonna stop people from taking the capitalist's factory? Private security? The state? Libertarianism (right or left variants) and anarchism are not synonymous.
C6: There is a definitional (semantics) issue with the concept of libertarian socialism.
R6: Yes, people argue over definitions all of the time. This vid still does not explain how a worker co-op or trade union would come for your house and would rather fearmonger about hypotheticals. The state can still protect personal property under this system.
C7: Motte and bailey argument: people advocating for worker co-ops are deliberately misrepresenting their positions.
R7: Prove it. People advocating for eating chinese food are deliberately misrepresenting their currently consumed meals. Just because I say stuff does not make it true.
C8: Socialism can only be defined as "the communal" ownership over the means of production and this means that for something to be called socialist, it must involve state ownership over the means of production.
R8: False. As per wikipedia, once again: "Socialism is an economic and political philosophy encompassing diverse economic and social systems[1] characterised by social ownership of the means of production,[2] as opposed to private ownership.[3][4][5] It describes the economic, political, and social theories and movements associated with the implementation of such systems.[6] Social ownership can take various forms, including public, community, collective, cooperative,[7][8][9] or employee." If worker co-ops are not socialist, then what are they? Are they capitalist? The vid hints at this, but does capitalism, as currently defined, accurately describe how they function? More importantly, is there anything in their operation or "essence" that directly contradicts the definition of capitalism?
C9: Fascism doesn't mean anything anymore due to overuse, but most agree that it is an extreme form of authoritarianism, which is the opposite of what the free market is.
R9: Ok, if it doesn't mean anything, then why not make it mean something and try to normalize this meaning? This statement about authoritarianism imply that a government which restricted every activity that you could engage in, except economic activity would not qualify as authoritarian.
In conclusion, there are valid criticisms that can be made about Libertarian Socialism, but the producer of this video failed to do so.