Total force exerted by the fluid on the surface is the sum of normal forces

In https://en.wikipedia.org/wiki/Pressure#Formula, the normal force per area $dA$ is $dvec{F}_n=-p,vec{n},dA$, where $p$ is the pressure. It is stated that, for any surface $S$ in contact with the fluid, the total force exerted by the fluid on that surface is the surface integral over $S$ of the right-hand side of the equation: $vec{F}=int_Sdvec{F}_n=int_S -p,vec{n},dA$. My question is why $vec{F}=int_Sdvec{F}_n$, and not $vec{F}=int_S dvec{F}$. I would like to understand why we sum the normal forces $dvec{F}_n$ at each point, and not the whole forces $dvec{F}$ at each point of $S$. Is it because the parallel component of each infinitesimal force $dvec{F}$ is $0$ ?