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When integrating, a [dummy variable](https://mathworld.wolfram.com/DummyVariable.html) is one that "disappears completely in the final result."

For example, in the expression $\int x\ \mathrm{d}x$, $x$ is *not* a dummy variable because the expression is equivalent to $\frac{x^2}{2}+c$, that is, the $x$ hasn't "disappeared."  If we had replaced $x$ with, say, $y$, then the result would change (to $\frac{y^2}{2}+c$).

But in the expression you wrote, $x$ is a dummy variable because the expression is equivalent to $\Gamma[n]$, and the $x$ has "disappeared."  If we had replaced $x$ with, say, $y$, then the result would not change (it would still be $\Gamma[n]$).

(Note that statistics has a different meaning for the term [dummy variable](https://en.wikipedia.org/wiki/Dummy_variable_(statistics)).)