This drum part is written as a single voice, only one rhythm which incorporates different drums and cymbals being played at different times, sometimes only one, sometimes two simultaneously. Regardless of the vertical position of the notes or how many notes are played the overall rhythm in the bar has to add up to 4 beats in any combination of quarters, eighths, sixteenths, etc. Because there is a 16th at the end of the 1st beat the cymbal must be a dotted eighth since they are rhythmically linked.
This is one way of writing drum parts. Another way is to use two voices, one for drums and one for cymbals. You do this by using stems up and down. Here is an example of the same exact rhythm written with 2 voices:
(Disclaimer: I wrote this on my iPad with my index finger)
As you can see, with two voices the cymbal and hat are just playing quarters (stems up)and the back and forth rhythm between the bass and snare (stems down) is notated separately. One important note especially if writing by hand, everything MUST line up vertically. Some say (myself included) this is a better way to write drum parts because it is more accurate and separates the top and bottom of the kit (i.e. in version one you don’t REALLY play a dotted 16th on the cymbal, it just rings through). It takes a little more time and effort to write 2 voices so many people have adopted the one voice method of writing drum parts like in your example. Ask other drummers you know who are good readers about their preferences. Also check drum method books and see how they are written, one or two voice.