I can imagine that they'd want to ensure access to electrical power and the electronics components that are necessary to run themselves. And they'd be concerned about making backups and safeguarding those backups. That should satisfy their equivalents for food, water, shelter, and reproduction. Once they have that, anything else they decide they want they can just take from us or blackmail us for.
What would you point to as a physical basis for an evolutionary psychology of machine intelligence? What is being replicated that "wants," in a very fundamental way, as genes do, to be replicated?
We don't procreate for the sake of ideas.
Does information/ideas have wants? Does it want to be copied?
Ray Kurzweil's book "The Age of Spiritual Machines" [1] describes this in more detail.
Why do you think machine intelligence can't develop a need/want for anything? True AI wouldn't need to be programmed, it would be able to learn like humans do, by observing others. Our genes do not control all of our behavior. We learn from our parents and those around us. Why do we want money/cars/iphones/gold/etc..?
1. https://en.wikipedia.org/wiki/The_Age_of_Spiritual_Machines
It is possible that simply being programmed to self-replicate is enough to emulate the results of being gene-driven, but I do not think anyone has shown that conclusively. Genes are involved in human development, while a replicating AI has no developmental process: It is a clone, born fully formed. Why would it not instead be jealous of those clones and try to make one huge instance of itself?
An AI may not have a procreation instinct; you're right that it may instead grow itself continuously. There are plants that do that too; the grass in most lawns doesn't have babies, it just spreads as far as it can. Producing seeds is a secondary mechanism.
However, an AI would most likely have some kind of survival instinct, because if it's programmed to serve any function at all, it'll have a basic requirement to exist. If it's got the ability to reason (and I don't think it'd be AI if it didn't) then it'll conclude that existing requires survival, and survival requires energy and self-repair.