Can "genocide" be used for the mass murder of disabled people?

You can examine the question from several directions. Start with the dictionary definition of genocide.

Dictionary Definition

Merriam-Webster defines it as the deliberate and systematic destruction of a racial, political, or cultural group. Dictionary.com defines it as the deliberate and systematic extermination of a national, racial, political, or cultural group.

The definitions are different. Does that mean one is right and one is wrong? No. A dictionary definition isn't a legal document like a contract or the governing laws of a country. Those kinds of documents are the original governing source of the meaning. They create the meaning and that meaning drives what happens in actuality. The dictionary is an attempt to describe a meaning that already exists in actuality, to capture its essence.

If it was a legal document, one might argue whether disabled people fit one of the listed categories, but that isn't the intent of the definition. It's intended to be more descriptive than a specific list of what groups can be considered as victims. The meaning of the definition is closer to, "the deliberate and systematic extermination of a large group of people based on a characteristic they share, such as national, racial, political, or cultural group." Disabled people would be included in that definition.

Actuality as the source

Referring to the Wikipedia article you reference, that describes the T4 program as stemming from the Nazi Party's policy of "racial hygiene", and goes on to describe the various components of their comprehensive ethnic cleansing effort. I would argue that given the unitary and comprehensive nature of the program, there would be little logic to separate one victim group from the whole and say the term "genocide" applies to all of the other victims but not them.

The Nazis didn't start with a dictionary definition of genocide and then create a program based on who fit the definition. It's the other way around. The definition of genocide is an attempt to characterize the scope of what the Nazis and others have done. The interpretation of the word should be driven by the actuality of what it describes rather than an abstract analysis of the definition's words. The Nazis defined their own program, and it included disabled people.

Conclusion

So to your question, I would say yes, “genocide” can be used to include the mass murder of disabled people, and a different term isn't necessary. I don't think it would be a valid argument to say that genocide does not apply to disabled people based on that group not being specifically listed in common dictionary definitions.

I agree with the excellent answer of @fixer1234, and will add a linguistic argument to support his answer.

From Etymonine genocide)

1944, apparently coined by Polish-born U.S. jurist Raphael Lemkin (1900-1959) in his work "Axis Rule in Occupied Europe" [p.19], in reference to Nazi extermination of Jews, literally "killing a tribe," from Greek genos "race, kind" (see genus) + -cide. The proper formation would be *genticide.

According Etymonline, genus comes from the PIE root *gene, as do the modern words gene and genetic.

The Nazis murdered disabled people who were born with disabilities -- people who had genetic disabilities -- not people who were disabled because of war injuries or accidents. See The Holocaust: A learning site for Students, The Murder of the Handicapped:

Wartime, Adolf Hitler suggested, "was the best time for the elimination of the incurably ill." Many Germans did not want to be reminded of individuals who did not measure up to their concept of a "master race." The physically and mentally handicapped were viewed as "useless" to society, a threat to Aryan genetic purity, and, ultimately, unworthy of life.

Thus it is a logical extension, linguistically, to call killing of the genetically disabled genocide.

Just like the other two responders so far, I also think that extending the meaning of “genocide” to include the mass elimination of the victims you describe is fine and would probably only be challenged by those engaging in or advocating the practice (and, of course, by pesky linguistic and/or legal purists).

If you did, however, want to insist on a separate term for it, you could consider hedging a bit by using the word’s adjective form in a two-word term like “genocidal eugenics”, for example, which is used, somewhat relevantly, in the linked NMU English paper’s title and body.

For a single word, you could even consider “eugenocide” (or it’s alternative spelling: “eugenicide”) which was used (and perhaps coined) by Richard Weikartin for the title of an article originally appearing in the July/August 2004 issue of Touchstone Magazine.

Wiktionary’s definition of:

eugenocide
Alternative forms: eugenicide
Etymology: Blend of eugenics +‎ genocide
Noun (uncountable)
1. The killing of weak or defective people in an attempt to improve the gene pool.
Usage notes
While the spelling eugenocide was used when the term was originally coined, the alternate form eugenicide is currently in more common usage

The term is also found, via Google Books, on page 117 of Yiannis Gabriel’s 2008 Organizing Words: A Critical Thesaurus for Social and Organization Studies, where it is included as part the “range of derivations from genocide [that] has been suggested” and where it is defined parenthetically as:

(the killing of people deemed not suitable to live within a given race, for example the mentally ill, criminal, homosexual).

A possible option is "democide", which is a blanket term meaning "the murder of any person or people by their government, including genocide, politicide and mass murder". As it's more general, it can cover cases "genocide" doesn't.