If we translate that sentence literally, it would probably be something like this:
"The rich are not limited to being always happy."
So 限らない expresses the meaning of 'not limited to'. Hope I'm able to help you understand.
"限らない Not exclusively" is by google
To my guess,
1. The rich are exclusively happy / to the exclusion of others
being questioned
https://freakonomics.com/2008/04/22/the-economics-of-happiness-part-4-are-rich-people-happier-than-poor-people/
2. but, not
In other sentence
The linguists are exclusively knowledgeable in this field.
But not, it is not decided by being professional / with degree or "amature"
shuben, it doesn't mean "The rich are exclusively happy / to the exclusion of others"
It means what HataReizu (and the OP's translation) said.
Thx for reply, Leebo
I was about to praise his Chinese...
The use of 限らない
限らない is used in a sentence context in which I can't really understand
Like this =>
金持ちが必ずしも幸福であると限らない。(The rich are not always happy.)
Can anyone bring in some insight?