I'm sorry but I'm going to talk more about survival.
Ace asks the Doctor why the Master tries to destroy people and the Doctor replies "malice".
Unsatisfied, Ace says "there must be more to it than that",
-and the Doctor amends his answer to "survival." The Master believes one day the Doctor will destroy him, and wishes to destroy the Doctor first. (The Doctor is evasive about whether the Master is right to fear him like this, saying "I suppose one day we might cancel each other out.")
Shortly after this, the Master makes a speech echoing the fascist ideas that the weak must be destroyed to allow the strong to survive that several of the human characters have been lured in by all episode.
There is so much to unpack there. We can talk about the uncomfortableness of Dhawan Master dressing up as a nazi and Simm Master joking about a 'master race' and enslaving Martha's family as a problem of new who not understanding what crosses the line from fantasy villainy into real-world horror that's hard to forgive, but survival is unambiguous:
The Master aligns himself with a facist worldview. And I think that's important, because that's what Rassilon and Tecteun do too. I think it matters that the Master's rebellion against the time lord high command eventually leads him right back to them. I think it's important that his desire to dominate drags him down into a belief in his right to dominate because that's what happens in real life. It is impossible to desire power over others neutrally. There is always a moment when you have to relinquish that desire for power or be changed by it. There is no third option.
Someone pointed out, and I immediately agreed, that the Master lays out his whole thesis in "Colony in Space" when he tells the Doctor: "one must either rule or serve."
Both of them want the same thing - to be free of the domination of the culture that bore them. That's why they make such good foils for each other. But the Master genuinely believes that the only path to freedom is Domination. He seeks to rule because he refuses to serve. But by the time he's Anthony Ainley, he's just seeking to survive, as you say - and he still sees Domination as his only path to that goal.
And when the Master in the end finally does return to gallifrey in the books he eventually takes command as president for life as the War King dressing all in black. He leads them into war against the Enemy and lets his subjects wipe out any lesser species they dream because they may one day rise up to challenge him.