It's based on the Unix timestamp, but it's counting milliseconds rather than seconds. (ES2015 calls this the "Time Value".) The Date object in Javascript uses this value underneath the surface. If you use the integer value as a parameter in the Date constructor, you'll get a Date object which should be handled quite well by most browsers.
const happyDateObject = new Date(1540920856937);
If you want a bit more control over what's going on, or want some more utilities that help you customize what the date looks like and how to manipulate it, I'd recommend the moment.js library. It's widely used because it's so useful. Since it's really just a wrapper for the standard Javascript Date object, moment objects convert quite easily to Date objects (when you need to do so). You'd construct the value in a similar way:
const happyMoment = moment(1540920856937)