I have merely attempted to give a very brief and very inadequate overview of human history.
The main thrust of this argument is however based in logic
There is no hint of logic, properly understood, in this landlord analogy. In the broadest sense, it is an argument by analogy. But the relevant disanalogies are so severe in this case that no one should rationally accept this argument as demonstrating anything. You seem to recognize this in your post, so I'll leave it at that.
But there is one flawed premise in all the arguments you put forth. The premise in question is a crucial part of the general Intelligent Design Argument. The ID argument is meant to show that the universe appears to have a design - a function - and the best explanation for this is that the universe has a designer. Notice the similarity of this argument to your examples of the mansion, computers, cars, and houses. Each of these has a designed purpose and so must have a designer.
But here is the flawed premise:
Having an intelligent designer increases the probability of the universe obtaining as it has - with all its properties that allow for life to form.
What supports this premise are notions like a tornado blowing through a scrapyard and randomly assembling a 747. The improbability of this is so high as to make it nearly impossible. But the inclusion of a designer who oversaw the construction of the 747 makes it far more likely.
But for this premise to be sound, the theist must present a reason for thinking that a designer would make the formation of our universe more probable.
In order to show this, we would have to have access to the designer's motives and abilities. Simply having a designer present doesn't, by itself, show the universe as we know it to be more probable than not. Let's say an expert woodworker is the designer in the scrapyard. Does this increase the probability of a 747 being constructed? Absolutely not!
The premise in question takes for granted two critical and very contentious assumptions: 1) the designer was capable of making our universe, complete with all its crucial features, and 2) the designer wanted to make our universe, and did so for particular reasons.
Now, positing a perfect, all-knowing God can easily explain the first assumption, but not the second. Suppose God exists and is just sitting in nothingness. God hasn't created the universe or anything within it. As a perfect being, what is God's motivation for creating anything at all? If this perfect being wants a perfect universe, then it already has that simply by its own existence. Why create additional, less perfect things to fill up a void? Did God lack something? Hopefully not - if God lacked something, then God would fail to be perfect. There doesn't seem to be a reason for God to produce anything at all - so how does this increase the probability of our universe obtaining given God's existence?
The only rational answer is: it doesn't. God's posited existence doesn't make this universe any more probable than any other. The theist can respond by saying that we can't understand God's motivations and so can't say why God would create this particular universe, or any universe at all. That's a fine response, but then the theist gives up the soundness of the crucial premise. If you have no idea why a designer would design something and actually have reasons to think he wouldn't design anything, that doesn't support the claim that the designer's presence increases the probability of a particular designed object's existence.
Honestly, I can't even get on board with claims that our universe is highly improbable. Proponents of this view claim that if anything had been different that the universe would be radically different from how it is - if it even existed at all. But how are we to know that the laws of physics (should they exist) didn't simply necessitate the formation of our actual universe? It's not a lottery drawing where it's easy to see how the numbers that came about could be different. We don't really understand the most fundamental aspects of our universe, so to claim that its formation is improbable seems unwarranted.
One last note on ID-style arguments. Many of them also work off the irreducibility of physical structures. Eyes and wings are common examples. These features don't make sense when trying to piece them all together - they only work when everything is there all together. So from an evolutionary standpoint, there is no environmental advantage gained from having these pieces until they're all formed. Therefore, some designer must have seen where this was all going and pushed it along that way.
But this line of thinking also has a critical flaw. Consider the process of building an arch from stone. You've got to have scaffolding to hold up the arch, but one you put the keystone in (the final stone at the top middle of the arch) you can remove the scaffolding and the structure will support its own weight. If someone came along and saw an arch and didn't know how it was constructed, it too would seem irreducibly complex. Not a single one of the stones in the arch could be there unless the whole thing was put into place at once - or at least the ignorant observer would think.
Just like the arch, however, the physical structures we see in nature might have also had some similar "scaffolding" that is no longer evolutionarily necessary. Structures like eyes and wings need not have evolved in the sense that we see them now. This flaw in thinking is due to a false presupposition that there is a design - an ultimate end - to a process like evolution. We now know this kind of thinking is simply false.
So, not only is a designer not needed to explain the universe as we know it, but having a designer doesn't seem to help explain our universe's existence.
