Rayman 2: The Great Escape.

I haven't seen it mentioned and I can't speak from first hand experience yet but the TBS Moonbase Commander is described as easy to learn, hard to master on the GOG page but that could just be marketing speak. Although it is made by humongous who makes many easy kid friendly "Edutainment" adventures(which were mentioned above).

11 year old girl and no one has mentioned the Creatures series yet? :) They''re adorable, and cover the basics of a lot of strategy while having a very low amount of violence.

The Creatures games are a cross between raise-a-pet and RTS, with bonus AI theory thrown in. The strategy part is mostly base-defense, gear management and exploration. For example, finding a mud-gun and hooking it up to a door to drive off raiding critters from your base. Or grabbing a mud-gun and using it yourself.

Skill trees come in the form of teaching your critters words and training them to use machines. The raise-a-pet part is fun and focuses on interacting with the critters as small children - the player teaches them words and how to do things, takes care of health problems, etc.

Critters can teach each other once you get a critical mass of adult critters. I'd recommend Creatures Village, it's the kids version that's less complex and a lot of fun. That might be aimed too young for an 11-year-old, so maybe Creatures Exodus would be right, depends on how she handles complex interfaces.

I really liked Lord of the Realms 2 (started playing when I was 11-ish) - it's TBS, with a nice interface and the voice acting is reasonably good. Covers a bunch of strategy without overwhelming players. And the AI was predictable enough that battles weren't usually a challenge, plus I could auto-resolve if I was willing to sacrifice troops.

For puzzles, Logical Journey of the Zoombinis and Lost Mind of Dr Brain were great, but those aren't on GOG and I don't know about their compatibility with modern systems. There's a more modern Zoombinis game that was pretty good - Mountain Rescue or something like that? World of Goo is probably the best recent puzzle game, followed by Cogs.

FWIW, she may not enjoy RTS and strategy games. I didn't usually at 11, and they're not my favorite genre still. Are you looking for those because you think she'll enjoy them, or because you think they're a blast and assumed she would too? EDIT: More game recs!

to the moon, she will love it

Speaking as a girl who played Myst about that age? Probably not interesting unless Big Sibling is going to be playing it with her. It was interesting, but I mostly wandered around enjoying the pretty scenery and having a blast pressing buttons without much of a connection to a bigger story. There was a lot to look at, but not a lot that made me want to find out what happened next. After we started playing it as a family I got more interested in making progress. :)