Your equation that you list as the angular velocity of a dc motor is nothing more and nothing less than the conversion factor between rad/s and rpm. There's nothing in there that's inherent to the motor.
The reason the number of pole pairs shows up in the equivalent version for the AC motor is because there's a conversion between electrical frequency and mechanical rotational speed happening there too, but there is no such electrical frequency to deal with in a DC motor, as DC is zero frequency by definition.
Basically, the two equations are converting two different things. For the DC motor you're calculating mechanical rad/s from mechanical rpm, but for the AC motor you're calculating mechanical rad/s from electrical rpm (cycles per minute would be a more general word to use).