ZVS Driver - Why does so much current need to flow through the diodes?
The gate of a MOSFET is effectively one plate of a capacitor, with the other plate(s) being the internal semiconductor materials. In order to turn on the MOSFET this capacitor must first be "charged up". The speed of its charging is based on the current applied according to the formula, $$I=C\frac{dV}{dt}$$
If resistance was added on the MOSFET gates, the "capacitors" would charge up more slowly due to the decreased current, which would delay the switching of the capacitors. This is often undesirable, because if the transistors take too long to switch on then the switching would no longer be ZVS, as they would actually turn on a bit too late, potentially causing damage. I expect the resistor was selected as the maximum possible value for this particular design while still allowing the transistors to switch fast enough for the circuit to work properly.