I believe you have a fundamental misunderstanding.
As a general understanding, it is true that you need a closed circuit. This is most commonly taught by the use of DC circuits, which do require "visible" or "direct" connectors that show a completely closed circuit. However, as you move into AC circuits, you need to learn that even "incomplete" (open) circuits are (or can be) closed, via various capacitance effects.
You need to be aware that a capacitor is made of two separated conductors, and although they are physically separated, as far as AC is concerned, they are electrically connected. In other words, any time you see a capacitor (-| |-), as far as AC (or pulsed DC) is concerned, it acts as if the plates are shorted (-|-|-).
As far as the antenna is concerned, the top of the antenna is connected to one side of a "virtual capacitor and the other side of the "virtual" capacitor is connected to ground. Since the bottom of the antenna is also connected to ground (by various methods), a "closed" circuit is formed.
Using the circuit with the vacuum tube as an aid, if you use a "small" capacitor and connect it to the top of the antenna, and the other side of the capacitor to ground, you will form a closed loop antenna. This allows the electromagnetic waves to induce a small current in the loop antenna. This current then induces a voltage across the capacitor connected to the control grid of the vacuum tube. The grid and the cathode of the vacuum tube also form a capacitor, so as the grid charges and discharges, it controls (gates) a larger current from the cathode to the plate, thereby the changes get amplified.
The explanation for pulsing DC, is the same as above. The pulsing DC charges and discharges one side of the capacitor which induces a voltage on the other side of the capacitor... thereby the changes get amplified.