Is there a gap in an LED between the plates (post & anvil) or a wire (or are there different kinds of each)?
Answer 1:

Yes, there is actually a physical wire there. However, the wire does not short out the anode and cathode, it connects from the anode onto part of the semiconductor die.

Answer 2:

The wire is just a wire, it does not contribute to the light output of the LED. (Other than providing a necessary electrical connection)

Answer 3:

This is not a new LED design.

Further comments:

All of the light emitting function happens on the small part labeled "Semiconductor Die" in the figure. In fact, that is the only part necessary. You could produce an LED with just the die, and it would work just fine. Although it would probably be quite difficult to use, and fragile.

LEDs are a special type of diode that emit a significant amount of light under forward bias. There is no "gap" that electrons jump across.1 The "Wire Bond" in the diagram connects the anode wire on the LED package to the anode connection on the semiconductor die. It is called a "wire bond" because "wire bonding" is the method used to connect these wires. The purpose of everything else in the diagram is mechanical stability, or light focusing/defocusing.

1 Electrons do transition across the energy band gap, which is what causes them to emit photons, but this is not a physical gap, it is all within a single block of semiconductor material. The band gap is a part of the energy band model of semiconductors.