I can't say for sure whether or not this particular study used proper testing, but as a whole introversion and extroversion is not pseudoscientific.

Jung wasn't a good scientist, but he did a lot of studies and came up with a lot of theories, some of which happened to be at least partially correct. Also, you seem to be getting something mixed up because Jung defined introversion as an "attitude-type characterised by orientation in life through subjective psychic contents", and extraversion as "an attitude-type characterised by concentration of interest on the external object", whereas the more common energy focused definition is not from Jung at all - at least, as far as I am aware.

The big five personality traits, namely openness, conscientiousness, extraversion, agreeableness, and neuroticism have been shown to be consistent, even cross culturally.

There are limitations to that: like how it's an empirical observation, that other personality traits exist that aren't factored into those five, or that it's possible there are a larger number of smaller subfactors that make up those five traits, but ultimately they are scientific.