This is specificity.
Running builds cardio endurance, but you won't find the speed and precision of your gallop, side step and pendulum increasing as a result of this.
It's not building mastery and skill in the required movement pattern...
In order to increase the speed and fluidity of your boxing footwork you must continually practise boxing footwork.
To increase proficiency with the pendulum footwork pattern you must practise the pendulum footwork pattern.
To increase proficiency with the side step footwork pattern you must practise the sidestep footwork pattern.
To increase proficiency with the gallop footwork pattern you must practise the gallop footwork pattern.
This is training specificity.
You must practise X to get good at X.
Performing Y will not work the same movement pattern.
This isn't a boxing specific training principle, training specificity is apparent everywhere.
You may be able to squat 415lbs but in order to do a pistol squat you must start from the most basic variation of the pistol squat and become familiar with the movement pattern, there's no other way.
Specific Exercises = Specific Results
In order to get better at a certain exercise you must perform that exercise (or a variation of that exercise utilizing the same movement pattern).
The military press and the dumbbell shoulder press are a prim example of this.
Both of these exercises are a pressing movement targeting the deltoids, although the movement is similar you will find that in increase in strength on the dumbbell shoulder press does not equate to a increase in strength on the military press.
I experienced this firsthand several years ago.
I didn't understand.
My dumbbell shoulder press was up 15% but my military press did not progress at all.
My military press didn't progress at all because I wasn't military pressing frequently enough to build my proficiency in that movement under an increased load.
Implement Exercises & Movements That Support Your Goals
If you want to hit a 315lb bench press for reps you're going to be wasting your time if you're spending your days running long distances or performing pistol squats.
You will not hit your goals unless you train specific movements that'll excel you towards them.
Training Specificity Examples
Want to build a big and strong chest? You better be focusing on your flat barbell bench press, incline bench press and weighted dips.
Want to build core strength? Your regime better incorporate hanging leg raises & hollow holds.
Want to improve your agility and footwork for your upcoming boxing bout? Forget running, focus on your specific footwork drills e.g. the pendulum, side step and gallop.