A washed wok should be completely dry before storage. The cited cleaning guidance recommends heating it on the stove until it is dry and moisture-free, helping remove residual moisture and prevent rust.
How to dry the wok
After washing, apply heat until the wok reaches the condition described in the guidance: completely dry and moisture-free. Only then should it be stored.
The source does not provide a drying time, burner setting, temperature, or separate test for trapped moisture. Those details should not be guessed.
What to confirm before storage
Check that no visible moisture remains. The reader should also confirm that the wok is suitable for direct stove heating by checking any product-specific care instructions; the cited guidance does not establish that every type of wok can be heated this way.