It happens when you exchange one type of token for another, that's the point being made. Broadly: the gain is calculated any time the value of the property is realised by using it to purchase some other thing. Using the thing to purchase money is one way of realising its value, and makes the calculations easy; but when used to purchase some thing other than money, the transaction can be assigned a monetary value and that's used to calculate the gain or loss.

The example given of the guy that had NZ$1.6m - the tax became due when he sold his NZ$1.6m of tokens for what we must assume was NZ$1.6m of some other type of token. He should have calculated the gain at that point, set aside an appropriate amount of money for to pay the tax bill later, and spent only the remainder on the other tokens.