This summary is not the rule. The rule text controls.
When someone who lived outside New York dies but had property or assets in New York, the state's regular will and probate laws still apply to them, just like they would for a New York resident. This means the process for proving the will is valid, dealing with challenges to the will, and figuring out what the will legally means follows the same rules whether the person lived in New York or somewhere else.
The same idea applies to handling the estate itself. If a court in another state has already started the main probate process, New York can still open a secondary case here (called ancillary administration) to manage property located in New York. That secondary case follows New York's usual rules for administrators, executors, and other people managing an estate, unless a specific law says otherwise.
In simple terms, this rule makes sure New York doesn't need a whole separate set of laws for out-of-state residents. It just uses the same will and estate rules that apply to everyone else, with a few exceptions written into other parts of the law.