Is this just playful behaviour or are they unaware that it's their own body part ?
I will try to answer this. First of all we have to make a claim. This behavior can be found in many animals behaviors but it is much more common in dogs.
In cats there is a few reason for that:
Feline predators have a genetic desire to chase anything what is moving. So the chasing tail behavior can be just game for practising hunting skills.
But if this behavior doesn't stop after the cat grew up it might be a serious problem. Just like any compulsion behavior in general it might indicate that your lovely cat has obsessive compulsive disorder. If this is the case, your pet can become much more aggressive, hyperactive.