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I don't believe we are any more closely related to Chimpanzees than any other ape for the reasons I illustrated in my analogies regarding cousins, apples, and kumquats.

So how do you explain the way the ERVs show up in various species of ape, as though there was a family tree with people and chimps on the same branch?

Source

Are you willing to claim that the hypothetical designer is constrained by the rule that any ERV in both new world and old world monkeys must also be in every species of ape, including ourselves?

By the rule that any ERV in both orangutans and gibbons, which live in Asia must also be in every species of African ape, including ourselves?

If the hypothetical designer is constrained by the rules summarized in the diagram, why? Explain in detail.

If it isn't, then why do we find this pattern?

This is just the primates. The same sort of rules apply everywhere: artiodactyls, carnivores, you name it.

Here is another essay from TalkOrigins with a family tree for artiodactyls; among other things, it indicates that a genetic marker found in both pigs and whales will also be found in hippos and cows.

With all these examples, how reasonable is doubting "common descent"?

Note that there's nothing on the branch between humans and chimps

From your source:

All branches after the insertion point (to the right) carry that retroviral DNA - a reflection of the fact that once a retrovirus has inserted into the germ-line DNA of a given organism, it will be inherited by all descendents of that organism.

These four constitute the argument:

ltr21q22.3
ltr41
ltr32
ltr21q22.2

There aren't any notations for retroviral DNA on the branch between chimps and humans, so claiming humans more closely related to chimps than Gorillas isn't supported by your chart.

The classic primate "family tree" excluding a few early branches looks like this:

Your source would split out the Orang and Gibbon, but that's not the way he drew it. Which leads me to believe he is pushing the humans descended from chimps* button as hard as he can.

*And he'll get around to bonobos in due time.