Really hard to build an empire without it.

Because to have an empire, you have to rule over a lot of people. Many of those people would rather not be ruled by you. If you want to force them to accept it anyway, you're going to need some of that genocide, slavery, and especially bloodshed.

Though, I suppose, maybe 2/3 of those aren't really necessary.

• Genocide probably isn't absolutely necessary to empire-building. Definitely still have to kill lots of people, but there's no particular reason you need to do so on the basis of race or ethnicity. (Though if you count cultural genocide as well, that may very well be necessary to build an empire. Difficult to bring diverse peoples under one banner without suppressing their cultural differences.)

• Slavery is a big probably. It certainly does help -- after all, your growing empire will need lots of labor, and it's unlikely you can afford to pay the going market rate for it. Plus, if you don't use slavery, you'll probably be out-competed by other potential empires that are using slavery and/or slavery-adjacent labor practices. But I suppose it's not technically absolutely necessary. Theoretically, at least, you could build an empire without slavery.