Remove the [FANCIFUL] tag. In order for COMMON_DOMESTIC to work, a creature must be [NATURAL]. GENPOWER doesn't seem to be a valid token. You need to give your creature make and female castes so it can reproduce, not sure if that will affect its availability tho... Is this a pre-0.31.xx creature raw? It must be, it doesn't have any tissues, lol. You'd be better off editing one of the creatures from the current raws into a pet than trying to migrate your raw like this if you don't know how. You have a bunch of deprecated tokens, and are missing a bunch of necessary tokens
Also, for new creatures to show up on embark, you have to generate a new world (your existing civilizations don't have any of the creatures).
Also strictly speaking, yes COMMON_DOMESTIC adds animals to the embark screen, but that's not all it does, and its not the only way to get them there. COMMON_DOMESTIC also makes all other races have them, and makes them show up as pets with your immigrants. If you give it the creature a biome, subterranean for example, and add USE_CAVE_ANIMALS tag to your civilization, they will appear on the embark screen, and only civs with USE_CAVE_ANIMALS will have access to them, and they won't show up with your migrants. I don't believe there are any other subterranean pets, so you don't get other animals that way, either.