I guess another way to put it is that "i.e." is more specific while "e.g." is more general. So "i.e." carries an energy of "I am referring very specifically to the following" while "e.g." means "there are other things that I'm not mentioning". So the use of "i.e." in the Tumblr post would imply that "tattoo", "sushi", and "guillotine" are the only loanwords in the English language.

To add to the explanations, here are some examples that might help:
There are various transportation methods, e.g. cars

There are various transportation methods, i.e. ways for a person to move from one location to another