I think the OP's problem here might be with the way the "$\dots$" notation is used in mathematics, to indicate a sequence (in this case the sequence of factors to be multiplied) by listing the first few terms and (if the sequence is finite) the last few terms, leaving it to the reader to mentally fill in the rest (on the assumption that the desired pattern will be clear). When this notation is used for a sequence that might be fairly long (for large $n$ in the case of $n!$) but might also be quite short (for small $n$), the result is that the explicitly listed first few terms and last few terms might, in the case of short sequences, be more than the terms actually intended. The rule for understanding this notation is to figure out the pattern and then interpret it, even in the case of short sequences, as beginning and ending as indicated but, in between, following the pattern, not necessarily including all the terms that were written to show the pattern.
Thus, in the case of $n(n-1)(n-2)\cdots3\cdot2\cdot1$, the pattern is "start with $n$ and count down (decreasing the factor by 1 at each step) until you reach 1". For any $n\leq5$, that will involve fewer terms than what is written. For example, if you take what is written literally for $n=4$, you'd get $4\cdot3\cdot2\cdots3\cdot2\cdot1$, but the correct interpretation does not repeat the $3$ and the $2$. When $n=2$, the literal reading is even worse, since the factor $(n-2)$ is then $0$, but the intended meaning is still "start at $n$ and continue to $1$", so you get $2\cdot 1$ (not $2\cdot1\cdot0\cdots3\cdot2\cdot1$).