Regarding: "age would be a class": Yes, in a sense. But that class can be broken down in various ways, all the way down to "classes" of one-year age increments, so it's not automatically obvious what the relevant categories are.
I think the terms you listed correspond better to the idea of "life stages" - and as you noted, terms like feticide, infanticide, and so on would apply. As MetaEd notes, those terms do not necessarily mean killing all members of those life stages. To denote such killing, I would imagine the only way to do that is to use a prefix term such as mass infanticide or complete senicide.
And a very generic way to describe these terms might be generational annihilation, generational extermination, or something like that.
EDIT BASED ON THE COMMENTS TO MY ANSWER:
OK, let's get to a mutually accepted definition of genocide to start with. According to Wikipedia, genocide is: "intentional action to destroy a people (usually defined as an ethnic, national, racial, or religious group) in whole or in part." If you have a different definition in mind, please post it.
But I guess you are interested in an umbrella term for genocide based on age in general, under which the specific subclasses (however narrowly or broadly defined) would fall. I would call that umbrella term "age range" or "age catgeory."
So one option is genaricide, loosely based on the suffixes used for octogenarian, septuagenarian, etc. But that's more about the suffix and does not actually include reference to the term age or age group. I found some Latin terms that are roughly equivalent to "age group," such as aetas coetus or simply aetate, but perhaps someone is better at finding a good Latin or Greek equivalent to the general term age-group-icide, which I think is what you're looking for.