Note: I didn't have a quick answer when I started looking into this so this particular answer is rather overkill. The last section contains the actual answer so you can safely skip down to the bottom. The rest of this post is me more or less documenting how I went about arriving at the final section.
Firstly, "build out" is relatively uncommon. Comparing NGrams of the various words that appear after "build", "build out" doesn't make the top 10:
- build a
- build up
- build the
- build on
- build and
- build an
- build their
- build upon
- build it
- build his
Even when restricting the following word to only prepositions, you still don't see "out" in the top 10.
So if this phrase is becoming more common, it is a very recent phenomenon and hasn't been picked up by the NGram data yet.
Secondly, when "build out" is used, it is usually followed by "of" as in, "build out of clay". The next most common uses are "build out the" and "build out a" which would seem to match your examples and/or match the examples from the linked question: "Build out" versus "build up".
So, not only is "build out" uncommon, "build out a/the" is even less common. And even when it does occur, it is usually a usage that matches the straightforward meaning from the "build [noun] out".
Even your examples can simply be reworded to match this usage:
Google... is also set to build a network out in Austin, Texas.
Technology services firm Data Stream has signed a 7,882 sq ft lease at the Chicago Board of Trade Building, where it plans to build a data center out.
This is a free series on how to build a website out using Wordpress
Each of the three examples are slightly harder to read, in my opinion, which perfectly explains why "out" was moved next to "build".
All of that being said, however, the core of your question is still valid. There does seem to be some distinction between using "build out" and "build" and none of the above explains why the writer included "out" in the first place.
CodeWarrior offers a solid explanation in the comments:
I have always heard "build out" referring to a planned build, and a "build" referencing an approved, ongoing, or completed build. For example, "He showed me the build out for the new server farm." vs. "It took us a week, but we finished the server farm build."
But this changes "build out" to a noun which is not at all what your examples are doing:
We have planned a build out.
We have planned to build out.
The NGram data shows us that "to" is the most common word before "build out" and even beats all VERB and NOUN combinations combined.
Therefore, I claim that "build out" is used in place of "build" simply because they are describing a particular type of build. This build type doesn't quite fit the definition accepted in the linked question:
build out usually refers to finishing the interior of a building or an apartment that one is renting or leasing.
To find an a more appropriate definition, we actually need to look at the definition of the noun mentioned by CodeWarrior:
Build-out is an urban planner’s estimate of the amount and location of potential development for an area. Sometimes called a "lot-yield analysis", build-out is one step of the land use planning process. Evaluation of potential development impacts begins with a build-out analysis.
build-out — the development and expansion of something, esp. of land
Thus, the phrase "build out" is used as a verb to describe the action of implementing such a build-out. If you slip this definition into your examples, the meaning translates perfectly:
Google is also set to [develop and/or expand] a network in Austin, Texas.
Technology services firm Data Stream has signed a 7,882 sq ft lease at the Chicago Board of Trade Building, where it plans to [develop and/or expand] a data center.
This is a free series on how to [develop and/or expand] a website using Wordpress
(3) seems slightly odd to me, but that actually matches my initial reaction when you used it as the third example. (1) and (2) are better examples of this particular usage.