Please explain why and how +new Date(); works as ‘workaround’ for Date.now() in IE8 or below

What happens is that you first create a new Date object and then cast it to a number.

TL;DR-version

Under the hood the runtime calls valueOf method of the Date object.

Verbose-version

return a new Date object

var d = new Date;

use the Unary + Operator

var n = +d;

The unary + operator calls the internal ToNumber with d.

9.3 ToNumber

Takes an input argument and if the argument type is Object (Date is) call the internal ToPrimitive with input and hint Number.

9.1 ToPrimitive

takes an input argument and an optional argument PreferredType.

if input type is Object the spec says:

Return a default value for the Object. The default value of an object
is retrieved by calling the [[DefaultValue]] internal method of the
object, passing the optional hint PreferredType. The behaviour of the
[[DefaultValue]] internal method is defined by this specification for
all native ECMAScript objects in 8.12.8.

8.12.8 [[DefaultValue]] (hint)

When the [[DefaultValue]] internal method of O is called with hint
Number, the following steps are taken:

1. Let valueOf be the result of calling the [[Get]] internal method of object O with argument “valueOf”.
2. If IsCallable(valueOf) is true then,
   1. Let val be the result of calling the [[Call]] internal method of valueOf, with O as the this value and an empty argument list.
   2. If val is a primitive value, return val.

In code this approximately translates to:

var val,
    type,
    valueOf = O.Get( 'valueOf' );

if ( typeof valueOf === 'function' ) {
    val = valueOf.call( O );
    type = typeof val;
    if ( val == null || type === 'boolean' || type === 'number' || type === 'string' ) {
        return val;
    }
}

[[Get]]ting the internal method of O with argument “valueOf” basically means returning Date.prototype.valueOf.

15.9.5.8 Date.prototype.valueOf ( )

The valueOf function returns a Number, which is this time value.

If we now go back to 9.3 ToNumber we see that ToNumber calls itself, this time with the returned val from 8.12.8 [[DefaultValue]] (hint) as primValue. If argument type is Number it says:

The result equals the input argument (no conversion).

The End