I think both the anime and manga combined to explain Algard well. He didn't want any of this, not being a king, not being forced into an arranged marriage, not being called a spare to someone who gave up the throne. And as you've seen, his parents aren't exactly good at listening to him either (fuck it, listening to either of their children), and Anis is also...never really around her brother at some point. Everyone contributed to the falling dominos getting more and more severe until the echo chamber and the abusive circle of liars and conspirators around him convinced him to go down the deranged route he's in. Lainie might be cursed with vampirism, Anis might have no magic, but Al is the one most chained down of all.
So yeah, TLDR he's jealous of his sister, but I can definitely see myself going down the same path if I were him. Think Harry and Meghan but Meghan are the side dudes taking advantage of Al.