My only exposure to the myth was the old Japanese tv show “Monkey”. I think they included a lot of that but while Monkey was prideful he came across more like a cocky but loveable jokester than the ignoble braggart you and the game appear to be describing.
I haven't watched that so I have no idea what their portrayal of him is like. Honestly, he's been told and interpreted in countless ways in various media.
Maybe I'm exaggerating a little or have a biased view but lets go over a little of his backstory.
He's originally a monkey born from a rock. He's happy, get along with the other monkeys on the mountain he was born until he witnesses the death of one of his fellow monkeys. This leads him to search for immortality and leads to him training under a Taoist master. He gets powerful and becomes rather prideful.
He decides he needs a weapon worthy of himself, so he rocks up to the palace of one of the Dragon Gods controlling the seas and demand they give him something. Nothing satisfies him and he eventually gets his signature staff which is actually one of the pillars holding up the seas. He also extorted a bunch of other artifacts from there.
The gods aren't too happy about some random upstart going around stealing stuff so he's sent to hell. But he's too powerful so he ransacks hell and erases his name and those of his fellow monkeys from the books containing the recorded lifespans of mortals.
The gods then decide he's too much trouble and offer him a place in heaven and decide it's better to try to keep him in control. Yeah sure the gods were looking down on him and basically gave him a low honorary position and it was pretty patronizing. Wukong eventually realizes this, gets upset and decides to just wreck the place. Fun thing here is that the execution attempts used by he gods on him just made him even stronger. He also stole and consumed other immortality granting macguffins such as the immortality peaches and elixir of longevity.
When Buddha shows up, he straight up challenges the Buddha which leads to his eventual loss and being pinned under the five fingered mountain where he had to wait 500 years for the arrival of Tang Sanzang.
Most of the above conflicts were basically instigated by him. Also throughout the Journey itself, the guy had loads of anger issues. Granted he was right a lot of the time, he had mystical eyes that allowed him to see through demon disguises but his master just saw a mad monkey trying to beat up innocent humans. Maybe his master should've trusted him more, but Wukong should've learned to be a bit more diplomatic about such issues too.
Maybe he's not as terrible as I'm making him sound. I don't think he's outright villainous or completely malicious, but he's not quite just a loveable jokester either. He is fairly omnipotent in terms of his powers which has led him to pride and hubris.