Its possible they only have hard evidence of second-degree murder at this stage, so rather than risk the guy being released due to lack of probable cause for first degree murder they can just bring a charge with fewer elements to prove and then add first degree murder later when they have gone over the evidence more.
After all, maybe he didn't originally intend to kill the guy, he did start by tasing him.
NYC law makes a first-degree charge a little more difficult even with premeditation. You need aggravating factors such as murder in the process of another crime (robbery, kidnapping, arson, rape, ...) or if the victim is a cop, judge, witness, etc.
Prosecutors can always upgrade charges later as more evidence comes in.
Having to refile with lesser charges gives the defense an advantage because they can tell the jury "look even the prosecution doesn't believe they have enough evidence of my clients guilt!"
