abbreviations - Using 'e.g.' in place of 'for example'

I'm looking at a text that regularly uses "e.g." in place of "for example", such as the following:

"This parallel composition can be transparently split between two cores, allowing, e.g., for faster execution".

(Ignore what the sentence is about. It's bogus and completely made up.)

The use of "e.g." in that sentence sounds really wrong to my ear, but I'm trying to understand why it is so.

I don't find a lot on the topic. I've been searching online, and on stackexchange, for posts that justify why it is or isn't wrong. Most posts and questions ask about the difference between 'i.e.' and 'e.g.', or try to explain the etymology of "e.g.", or present positive examples (e.g., 'use it when enumerating'), but present no examples of wrong usage.

Can anyone explain if the above usage is wrong, and a reputable source that clearly explains why?

Also, is there an appropriate rule of thumb to understand which cases are wrong? I can think of the following: If you cannot remove "e.g.," and the example(s) that follow and obtain a grammatically correct sentence, then it's definitely wrong. However, even if this rule of thumb is correct, it's not complete. For instance, I cannot replace the use of 'for example' at the beginning of this very sentence with 'e.g.'

Near duplicates:

I've left a comment in one of those because the answer agrees with what I say but does not really explain why. However, the answer has already been accepted, and I doubt there would be any activity at this point.