Telling one person that they can help out by not having kids is rather different from, as the dictionary says

Your definition seems to be quite limited. Many acknowledged genocides would not be treated as such. According to Wikipedia, the UN Genocide Convention is much broader:

Genocide is the intentional destruction of a people[a] in whole or in part. In 1948, the United Nations Genocide Convention defined genocide as any of five "acts committed with intent to destroy, in whole or in part, a national, ethnical, racial or religious group." These five acts were: killing members of the group, causing them serious bodily or mental harm, imposing living conditions intended to destroy the group, preventing births, and forcibly transferring children out of the group. Victims are targeted because of their real or perceived membership of a group, not randomly.[1][2]

Spreading an ideology according to which one shouldn't have kids, thus preventing births, would fall into this definition.

Even suggesting to a whole group of people not to have kids is not the same as killing them.

You are correct, it is not the same as killing them, but no one was arguing that. Again, limiting genocide to the deliberate killing of individuals would be quite a lenient definition, and various laws that targeted various ethnic minorities would not be considered genocides, despite them being considered as ones and having the same exact effect. Consider forced sterilization. You don't have to forcibly kill anyone, yet probably everyone here would agree that it is a genocide.