Those aren't broad definitions at all! Quick question though, what is "acting", what is "thinking", what is "rational"? Your definition of intelligence practically includes the term in its definition(s).
I like the acting human approach (Turing) because it can be stated more precisely. One test is the classic Turing test -- fool a human judge.
Another line for acting human would be the ability to self direct learning in a variety of situations in which a reasonably intelligent human can learn. That means a single algorithmic framework that can learn go, navigate a maze, solve Sudoku, carry on a conversation and decide which of those things to do at any given time. The key is that the go playing skill would need to be acquired without explicitly programming for go.
I believe a lot of our intelligence is the ability to perform solved AI problems given the situation. The key is combining those skills (whether as a single algorithm or a variety of algorithms with an arbiter) and the ability to intelligently direct focus. That's why most researchers aren't confusing alphago with general intelligence. It can play go - period.
1) Acting like a human (this is the Turing test approach)
2) Thinking like a human (this is cognitive science, and for now is focused on figuring out how humans think)
3) Thinking rationally, ie, following formal logic (the difficulty here is encoding all the information in the world as formal logic)
4) Acting rationally. That is, entities that react rationally to their goals (this one is notable because it allows fairly stupid entities).
These are all explained in more detail in Artificial Intelligence, a Modern Approach by Russell and Norvig