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.

An embryo goes from a single cell to multiple genetically identical cells, that is replication. Sperm cells do not replicate into more identical sperm cells, eggs do not replicate into more identical eggs.

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.

I would argue that the mitosis process sperm cells undergo splits the cell into two genetically different cells and the genetic difference ia not a mutation so it’s not replication. Egg cells don’t replicate they don’t copy their DNA, they fuse with sperm at which time they become an embryo and start to replicate.