The guy at the tyre shop tried to convince me that my tyres need replacement. My car is just above 2 years old and I plan to change them after 3 years. Please have a look at the picture and advise.
It really depends on how old they are. You state your vehicle is two years old (or at least I'm assuming that). Your tires could be much older, so you'll have to determine the date code on the tire itself. Tires should be no older than 10 years, while some manufacturers state six years is the maximum. This usually doesn't come into play as tires wear out (due to mileage) well before this time limit occurs.
To read the date code, look at the following image:
The date of manufacture is the last four digits of the DOT code. The first two digits are the week of manufacture, and the last two digits are the year. For example, if the last four digits of the DOT code are 0203, that means that the tire was manufactured during the second week of the year 2003.
For the above image, the tire would have been made the 16th week of 2012.
Small cracks like those in the picture are, in my experience, normal. Although I can't be certain just by looking at a photo, the tread depth seems pretty OK too, so there should still be enough life left in your tyres - provided they're not too old, as already stated in the answer by Paulster2.