Considering those quotes talk about defining “living systems” or “groups of organisms”, as opposed to individual cells (and again, elaborated on even moreso within the full linked articles), I’m gonna have to say “no, they’re not really excluded at all.” Their entire purpose is to meet up and initiate replication. An egg and sperm cell are each one small part of a much larger system of ongoing life. The same can be said for a fertilized egg, an embryo, and so on for most stages of development in a womb.

If you want to insist on a definition that says egg and sperm cells aren’t alive, or aren’t an organism, you’re gonna have a hard time saying that a fertilized egg or an embryo are. They don’t replicate on their own, either, not without a very specific environment and set of stimuli.

Also, sperm cells DO replicate, to an extent. They undergo forms of mitosis and meiosis, during their growth. And an egg cell absolutely replicates. Like any other type of cell replication, it needs certain stimuli to initiate it. I.E. it needs to be fertilized.