
There's multiple points in this story where Wookyung should've used the safe word. Its supposed to be there to keep you safe and establish a trusting relationship with your partner.
Wookyung is too anxious about 'pleasing' his dom that he isn't taking himself into account, which is common for most newcomers in BDSM. He thinks that by using the safe word everything stops (the play and the relationship) and there'll be some kind of disappointment. In reality, people tend to have multiple safe words/actions; which indicate "i need a break", "slow down" etc.. Its heavily important.
Wookyung and 'Sir's dynamic is in 9/10 cases what NOT to do in a BDSM partnership