The Vijayanagara Empire was destroyed in 1565, barely eight years after Akbar had won the second battle of Panipat and started the second innings of the Mughal Empire. At that time the European powers were confined to certain trading posts and the peak time of the Mughals had not yet arrived. The contest for the supremacy in the subcontinent, as we understand commonly took place after the decline of the Mughal Empire. That might be the reason why the Vijayanagar was not included. The states mentioned are all the states that existed in this particular period.
If you consider in a broad way, the contest for supremacy in different parts of the subcontinent had gone on between several powers through out the history. Magadha, Kosala, Mauryas, Kalinga, Cholas, Cheras, Pandyas, Satavahanas, Kushanas, Guptas, Vakatakas, Vardhanas, Chalukyas, Yadavas, Rashtrakutas, Gurjaras, Pratiharas, Palas, Pallavas, Kakatiyas, Kadambas, Hoysalas, Several Rajput dynasties, Several Sultans, Nawabs etc. were all players in the game. The given list involves only a particular period and the Vijayanagar does not belong to this time frame.