In the U.S., "judge only trials", usually called bench or non-jury trials, are available in all jurisdictions. In criminal cases, in some states, including New York, it is entirely up to the defendant (except for first degree murder), in others, both the defendant and the prosecution have to agree. This guy will be charged at most with second degree murder. First degree murder in New York State is limited to certain circumstances that aren't present in this case.
https://www.arthurpressmanlaw.com/exploring-the-different-degrees-of-murder-charges-in-new-york/