Present continuous is used here because 'the enjoyment' or 'non enjoyment' is continuing and hasn't finished.
By using present continuous in this example, the speaker is essentially telling us he has not yet given up on listening to the record. The speaker could have used the present tense and said 'I do not enjoy this record'. This version is valid, but speaks more of the present instant. It gives us no clues whether he will continue listening or not.
But when he says 'I am not enjoying this record' he is speaking more of his ONGOING enjoyment/non enjoyment of the record and this ongoing action has not yet finished. So the speaker is also telling us he is not finished with the record. The present tense version above does not tell us this.