ha ha.. it's a tricky example.
I think you understand the first sentence incorrectly.
'She doesn't really think of me that way' seems to mean;
"She thinks of me as her prince.... nah, only joking; she doesn't really think of me that way"
(really = it's true)
It could mean what you think, but I wouldn't think so if I hear it.
In the second sentence, 'really' is used for emphasis (not only that it's true), like 'I really don't like her' = I almost hate her.
So, you are emphasising the point;
eg, if you hate a guy: "hey, you like him, right?" 'NOoo, I really don't!'