I am absolutely in love with Mo Xiuyao and the emperor's first scene because plot-wise it doesn't really do much. Mo Xiuyao and the emperor make up in the very next scene they have together. But character-wise it does a lot in a way that makes me excited about the writing in the rest of the show.
The important thing here is that the emperor made a mistake. He didn't trust Mo Xiuyao and that cost the life of one of his officials and more importantly the vital information that he was carrying which could have exposed Muyang's crimes. And now taking power away from him and his faction is going to be that much harder. And the emperor knows this and Mo Xiuyao knows this, so going into the conversation, the emperor tries to apologize without actually having to apologize, and move past the problem.
(See how he subtly tries to shift the blame away from himself? It was because he was afraid, it's not his fault he doesn't know who to trust. And "what's done is done" is such an interesting line from the person who did it.)
But Mo Xiuyao is not having it. He's justifiably angry, and he needs to spell out for the emperor exactly what his mistake has cost them.
(So nice to be reminded so early in the series that Cheng Lei can act)
And it is important to note that he is entirely correct for this. The emperor made a huge mistake, and nothing that he says is wrong. However, a character with a little bit more tact probably wouldn't have started shouting at the emperor, and instead would have used this as a chance to seize the trust that he had just been denied and continue with his plans.
Alas, Mo Xiuyao is not that character, and the emperor cannot handle being yelled at no matter how justified it is, so he lashes out at Mo Xiuyao.
And it's interesting to me that that's the end of it. The next time we see them interact, they are being much more civil towards each other. Mo Xiuyao has calmed down enough that he is ready to accept the emperor's trust with his own list of demands, and the emperor seemingly doesn't hold his outburst against him and gives him everything he asks for. They go back to working together.
In a different drama (imo a lesser drama) an argument like this would have been cause for a major conflict between Mo Xiuyao and the emperor. Here it seems to just fizzle out (although whether there is some lingering resentment on either side remains to be seen). But this scene is still very important for establishing both of these characters and more importantly their relationship.
For Mo Xiuyao we learn that:
He is a very angry character (not new information) but more importantly that he is angry in a way that will cause him to lash out and act rashly, even in front of the emperor.
He still has a sense of loyalty and honor, even if it is mostly directed towards causing the downfall of his and his brother's enemies.
He feels guilt for what he sees as the role he played in his brother's death.
Most interestingly, despite being of a disgraced household, he still has enough status to go into the palace and yell at the emperor.
And for the emperor we learn that:
He is still very young and inexperienced and prone to making mistakes.
He does not want to own up to his mistakes.
He will lash out when he feels like he's backed into a corner.
He either has enough goodwill towards his cousin, enough sense to realize he still needs him, or not enough power in his position, (or some combo of all three) that he lets Mo Xiuyao leave without doing anything to retaliate.
I am fascinated by the writing of the little emperor. He is a complex character, which I feel like is rare to see from a child emperor character like him. And I am super excited for the writing in this series that will let the characters have a scene like this just for establishment.