If I was HR Head of Company 'X', I would definitely write to Company 'Y' on this subject because it is a breach of trust not only with Company 'X' but Company 'Y' also (because you have told Company 'Y' that you were relieved by Company 'X').
If you had fulfilled your side of commitments and still Company was not relieving you, then it would have been fine to join Co. 'Y' without getting relieved, but from what you have stated it looks that you have not done so.
Again if I was HR Head of Company 'Y', I would take it seriously because if you can do it with Co. 'X', you can do it with Co. 'Y' also and ultimately both are employers.
KKT