Could anyone please explain, why the Holy Quran might have remained silent on religions apart from Judaism, Christianity and the Magian religion? Does that mean that Islam de-recognizes all these religions and considers their followers unbelievers, just as orthodox Judaism casts doubts upon  Islam?

It kind of leaves Hindus, Buddhists, Zoroastrians, Confucians, Shintos and Taoists, Sikhs and Bahais pretty much in the dark. It also gives followers of other religions the flexibility to align or misalign their beliefs with Islam.

Hinduism : Although the current versions of Hinduism are pretty much idolatrous, the ancient Aryan religion of Pakistan and India (which was then not known as "Hindu") was not. In the 6th century CE, when the Holy Quran was revealed, vedic worship of the one Supreme God was in force in Pakistan / India, although polytheism was also practised.
(Addendum) Among modern day Hindus, it is very difficult to turn people from their established ways and ask them to accept Islam. They tend to challenge my very question above. Also, because they were not directly given the Holy Quran, but have only received it as a result of bloody and painful 1000 years of history (compounded with the equally bloody and violent history of the Partition), it has led them to making a very, very sad association of the true Religion with violence. As a result, they believe that Allah (swt) has spoken to their angels and prophets and saints (many of whom they have incorrectly deified), and that Allah (swt) has not stopped sending divine messages even today.

Eastern Religions: Buddhists, Confucians, Shintos, Taoists, and other eastern religions, far from being idolatrous religions, many do not even have the concept of God. Buddhism and Confucianism, for example are a way of life, not a way of communion with God.

Zoroastrianism : The core beliefs are the very image of Islamic concepts. According to them, Ahura Mazda is the one true God, who is deserving of all worship. Is that not the Farsi belief in Allah and none except Allah? Why then, was Zoroastrianism destroyed so utterly?

New religions : Bahaism and Sikhism, which were founded by the Bab/Bahaullah and Guru Nanak respectively, are completely de-recognized by Islam. How can these religions be interpreted in the light of Islamic awareness? Is there no possibility that Almighty God Allah (swt) may have seen the developments in the world getting worse in the 16th/17th century, and may have wanted to send a message to his long-suffering people in some other part of the world? Are we saying that there will be no more divine messages (even short messages) from Allah (swt) after the last Surah was revealed to the Rasool Muhammad (pbuh) up until the Day of Judgment?

I think that because the Holy Quran is silent on all these religions, it is up to followers of these religions who have to decide, in conjunction with sincere Islamic scholars, how to best synchronize their beliefs with Islamic beliefs, if we are to think of religious peace and tolerance in many parts of the world where Ahl-e-Kitab's do not live. 

Addendum to Question: Does the Sunnah of the Prophet (Please forgive me I have not read the complete text) mention anything about these religions of the day?

If you do bother to analyze and reply, I thank you. Request you to please bear in mind the following : 

1. I love Islam.

2. I feel that the greatest happiness will be when every religion absorbs Islam or the core part of Islam into its everyday practices.

3. I believe that worship of God Almighty is after all, the most important aspect in one's life.

4. I am specifically referring to Islam vis-a-vis non-Book religions, i.e. Not vis-a-vis Judaism or Christianity, which is a much wider topic of discussion.