No, that isn't what the No True Scottsman Fallacy is. Putting qualifiers on statements is completely valid. A No True Scottsman Fallacy is when you use qualifiers in a hand wavy way to move the goal posts.
What makes it a No True Scotsman is the term 'sufficently random', which kind of makes it unfalsifiable. After all, if any two shuffles are the same, then (by this logic) they're not sufficiently random.
Except its unlikely that "sufficiently random" refers to "do not equal each other" in this context. Its likely that "sufficiently random" means "passes one of a variety of proofs of being statistically random (for example: nlogn repetitions of fisher-yates)". That implies randomness, but doesn't imply "doesn't equal any other deck of cards" except with high probability.
That doesn't make it unfalsifiable at all. Sufficiently random is not defined as "not the same". you also clearly misunderstood the logic of the post in question. The poster started with a clear definition of random and used that to determine if shuffles are likely repeated. If there were fewer cards in a deck, that post would have reached a different conclusion.
