Do my Shimano 7900 Dura Ace chainrings need replacing? Basically today I had a bizarre suggestion; someone told me that my Dura Ace 7900 crankset (a 53 chainring) needs replacing because some teeth are worn from use.

I ask myself, is that possible? I've had Dura Ace before and the only thing I've heard about changing every once in a while is the (rear) cassette.

What do I have to do? Change my chainring, buy a new one for 200 euros? 
I believe it is impossible for people to buy cassettes and chain rings every year. I am not a pro cyclist to ride many thousands of kilometres a year!
You should be ok for training, but when the time comes to replace the chain the worn chain rings will speed up the degradation of the new chain. You should try to replace the drivetrain components all at once or you won't get maximum value for money. But this can be expensive and overkill if you're not cycling competitively.