Yes, they do, and it makes sense to do so. You want to point others to the related work that has been done in the topic and it's likely that your lab has done a lot of this work.

Of course other groups have also done related things, and you should cite them as well to create an honest image of the research landscape.

In the case the OP mentioned, this is how a lot of research is carried out. The main part that sticks out to me as as scuzzy is that he took first author without being closely involved in the work.

Isn't he roughly doing what PIs do? Except they usually take last author.

In CS and ECE, yes, PI is the last author.

But as a PhD grad looking for a faculty position, you will be evaluated by the number of first-author papers you have published.

Name order depends on the conventions of the field, but yeah.