Visualizing s and p orbitals from contracted basis set
Your suspicion is correct - you need the angular part, that is, a spherical harmonic (sometimes it may be cartesian instead) to get the shapes of the orbitals and thus, actual lobes of $p$-functions.

Also note that projection to $(x)$ from $(x,y,z)$ may not be straightforwardly the same for all angular momenta. Additionally, the angular part also has influence on the normalization of the basis functions, which may or may not be included in the basis set format at hand. The last point, however, can be checked by numerical integration.