I am currently studying the textbook A Student's Guide to Maxwell's Equations by Daniel Fleisch. In a section discussing the integral form of Gauss's law, the author says that the dot product in
$$\oint_S \vec{E} \cdot \hat{\mathbf{n}} \ da = \dfrac{q_{enc}}{\epsilon_0}$$
"tells you to find the part of $\vec{E}$ parallel to $\hat{\mathbf{n}}$ (perpendicular to the surface)".
Why does the presence of the dot product demand that we find the part of $\vec{E}$ parallel to $\hat{\mathbf{n}}$ (perpendicular to the surface)? The only degenerate case seems to be when $\vec{E}$ is perpendicular to $\hat{\mathbf{n}}$, which means that their dot product is equal to zero. Besides this case, I do not see why $\vec{E}$ must be precisely parallel to $\hat{\mathbf{n}}$?
I would greatly appreciate it if people would please take the time to clarify this.