Being a quantum mechanical object, it obeys uncertainty principle, but quantum computation does not derive its usefulness and functionality from uncertainty principle. The uncertainty principle in its usual form is a statement about 2 incompatible observables. In the standard model of quantum computation, there is only 1 single observable, in the form of a measurement made at the end of a computation. They are both interesting subjects but there is a clear difference. I don't understand why you are trying to defend a clear misconception rather than try to correct it.
The uncertainty principle is a popularized quantum mechanical concept but let us not overstate its importance and think that everything in quantum mechanics revolves around it.
His description isn't perfect but it doesn't say anything that's outright incorrect, unlike your statement that uncertainty is irrelevant and he's wrong for bringing it up. I could nitpick his answer but I'd rather correct much more apparent misconceptions in your criticism.
And just to be clear, I'm not talking about the "popularized" uncertainty relation (Heisenberg's relation between position and momentum), I'm talking about uncertainty in general - that is, that any pair of non-commuting observables can't simultaneously be in definite states. These take the form of commutation relations that are
routinely referenced in quantum computing literature.
There are three directions of spin and all of them are non-commuting (i.e. they are incompatible). The commutation relations for spin take the form you are talking about (as in, each one is a "statement about 2 incompatible observables").
These commutation relations show that every pair of spins has a commutation relation, which ultimately means that measuring one will impact the state of the others. In other words, even though the final result of a computation depends on one direction, the others play a central role in defining its states prior to that final measurement.
Lets say the observable you are interested in measuring at the end is the spin x direction. How do you think they prepare that observable to be in a superposition of states? Send a pulse in either of the other two directions. If either the y or z state is precisely defined, the x state will be in a perfect superposition of the |0> and |1> states. You can precisely control the x state by using using a combination of pulses (measurements) in the y and z directions. Manipulating the spin of a qubit in this manner doesn't work without the commutation relations you see above and it's central to certain forms of quantum computing (e.g. NMR quantum computing). More generally, many quantum logic gates exploit the commutation relations between spin directions to manipulate the state in the direction of interest.
Even basic theories of quantum computing refer to those commutation relations to describe the state of a qubit regardless of which direction they plan to measure in the end. Trudeau's statement that "uncertainty around quantum states allows us to encode more information into a much smaller computer" is essentially a simplified explanation of
qubit field theory, which defines the amount of information that can be stored in a single qubit (more accurately, a specific localized region of space) by using the commutation relations between observables in spacelike-separated regions.
tl;dr His explanation is somewhat sloppy but doesn't include any untrue statements, whereas your criticism revolves around an outright misconception that uncertainty and superposition are unrelated. Uncertainty between spin states is commonly used to manipulate a particular spin axis and place it in a superposition of states.
