Phong model: why no multiplication by N dot L in specular term?

The $N cdot L$ term (I've seen "geometry term" thrown around; not quite accurate, but good enough for here) is part of the rendering equation. What you're looking at here is an estimate of the inside of the rendering equation—that is, the incoming radiance i times the geometry term dot(n,l) times the BRDF.

The simple answer for why the Phong BRDF doesn't include the geometry term is "Well, it probably should, but the Phong model predates the invention of the rendering equation by more than a decade.".

Phong, B.T.: Illumination for computer generated pictures. Communications of the ACM 18(6), 311–317 (1975).

Kajiya, J.T.: The rendering equation. In: Proceedings of the 13th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ’86, pp. 143–150. ACM, New York, NY, USA (1986).

This deficiency was fixed in what is now called the Modified Phong BRDF:

Lewis, R.R.: Making Shaders More Physically Plausible. Computer Graphics Forum 13(2), 109–120 (1994)

At the end of the day, whether the term is present or not isn't an issue of correctness per-se. Not having the geometry term when you might expect it just means that the BRDF corresponds to a different surface reflection that doesn't foreshorten much at glancing angles. Indeed, many other BRDFs have terms that look like reciprocal geometry terms, so that they cancel with the actual geometry term in the rendering equation.

In code, the BRDFs look like:

vec3 f_phong    = rho_s/(TWO_PI/(a+1.0)) * pow(max(0.0,dot(r,v)),a) / dot(n,l);
vec3 f_modphong = rho_s/(TWO_PI/(a+2.0)) * pow(max(0.0,dot(r,v)),a);

And so when multiplied by the light and geometry term in the rendering equation (i.e., i * f * dot(n,l)), you get:

vec3 spec_phong    = i * rho_s/(TWO_PI/(a+1.0)) * pow(max(0.0,dot(r,v)),a);
vec3 spec_modphong = i * rho_s/(TWO_PI/(a+2.0)) * pow(max(0.0,dot(r,v)),a) * dot(n,l);

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The obvious should be noted, however: while the Phong BRDF is simple to understand and implement, it is of limited accuracy on real-world materials. It's not terrible, the way many people think it is, but it does lack important features that can be important on many materials. It is not the state-of-the-art, and depending on your needs you may like to look elsewhere (GGX microfacet, etc.) for more modern BRDFs.