I am wondering whether the word genocide can also be used for the killing of a group of people based on their religion, for example: 'the Sikh genocide'. I have never seen it used that way, I have seen 'Armenian Genocide', 'Kurdish genocide', so on and so forth.
Houghton-Mifflin defines "genocide" as the killing of "an entire national, racial, religious, or ethnic group". "Religious" in there would indicate that it could be applied to killing people because they are Sikhs.
Random House says its "a national, racial, political, or cultural group". No mention of religion. Perhaps Sikhs could be considered a "culture".
Merriam-Webster also says "national, racial, political, or cultural group".
But Collins defines it as killing "a nationality or ethnic group". Sikhs don't meet that definition.
The 1948 Convention on the Prevention and Punishment of Genocide defines it as "a national, ethnical, racial or religious group". (http://www.preventgenocide.org/genocide/officialtext.htm) Maybe that counts as an "official" definition.
(Note: The web page I cite said "ethnical". I assume they meant "ethnic". Whether that error is in the original document or was an error on the part of the people who made the web site I don't know. Just don't blame me.)
Yes, it can be used to label the killing of the members of a religious group:
The extermination or attempted extermination of all or part of a religious group would be recognized as genocide under both the legal definition set up by the United Nations Convention on the Prevention and Punishment of the Crime of Genocide and the common usage as found in the news media or dictionaries.
Part 1 of Genocide: A Comprehensive Introduction by Adam Jones (2010; Routledge) provides an excellent background on the coining of the term by Raphael Lemkin, its popularization and codification, and subsequent redefinitions offered by social scientists.