She's required to do various little things of the highest importance, but she does more various little things that she isn't required to do, and they are of the highest importance to him, though he's never said that aloud, or even written it down. He wouldn't risk it.
Her disdain for people and her affinity for snark are part of what got her the position she holds. She's amusing and she dislikes sentiment, in general. But she doesn't have it in her to snark much at Mycroft. She's playful, lightly teasing, but there's absolutely no disdain there, no matter how pathetic he believes he's coming across, no matter how much he seems to have screwed up.
She pulls out his chair for him. He's never asked her to, and he's certainly never told her to stop. He's done so for her before, which they both seem to recognize as a gesture of politeness. When she does it for him, it feels more like a declaration.
She opens doors for him as well, especially when they are alone together. When they are alone, she does a million tiny little things that she'd never do for anyone else. There are people she wouldn't piss on fire to save, far too many people for Mycroft's liking, sometimes. But then again, it's nice to be the one person someone will go the extra mile for.
She gives him little gifts. It's usually flowers, which smell sweet and brighten up his empty home. She doesn't send them to the office. Sometimes it's books, and he thinks of her when he takes a break to read them. Her tastes are a bit different than his, but she's fairly good at guessing what he'll like. He'll read anything she buys him no matter what because he wishes for her to know how grateful he is, even if he doesn't often bring her gifts into conversation. She prefers it that way.
Occasionally, she invites him to dinner, cooking for him. She's come to the manor to do so before as well. Her cooking is improving, and dinner is so much less lonely when she's around. The food is healthy and he eats well.
Sometimes they take walks together for a break from business. She'll go in front of him to pull aside tree limbs. He could do it, yes, but her smile as she does little things for him warms his heart, warms all of him. She makes him feel as important to himself as he is to the country.
Some could consider the little things she does to be an extension of her job. They aren't though; they're separate. She does them because she doesn't have anyone else in the world to be nice to, or so she believes. She does them because she thinks Mycroft is special. She cares about him very deeply, and it's clear as day, even if they don't talk about it.
She injects affection into each "sir", keeping the distance between them with the term while at the same time making sure he knows how she feels, even if they don't say it.
They think things are safer as they are, are okay as they are. They aren't in a rush to change things.
Some could call it duty, but it isn't duty. Plainly, simply, it is chivalry.