Do you think someone who is bilinigual ,trilingual or more does know how to discern pitch, rythm or tone?
Do you think they know necessarily how to carry out intricate mathematical operations?
Are they necessarily interacting effectively with others?
Is there spacial reasoning very much developed as their linguistic skills ??
The answer to all those questions is mostly NO, not necessarily.
That means one could be language smart and otherwise dumb ;)
A Howard Gardner detected 9 types of intelligence among them linguistic intelligence.
As a conclusion one might be word smart, but not necessarily smart in other domains.
There is no positive correlation detected between linguistic intelligence and other forms of smartness.
So word smart doesn't make anyone SMARTER than the nature smart, it is just different kind of skills developed.
Whether linguistic intelligence is naturally disposed and gentically predetermined is debatable.
Some studies detected that genes determine individual differences, and may shed light on the heritability of cognitive and linguistic skills.
I personally think it is a mixture of natural disposition and lots of efforts, pretty much as Aлeкcaндp states 'it is working the machine'. If you don't use it you loose it.