4000 random people does mean something, you can extrapolate the data with it, it's the whole point of surveys. Of course, the numbers won't be very accurate, but it gives a good approximate.
You're assuming that the set of people surveyed was truly random, but it never is—people who don't like answering surveys are always underrepresented (obviously), and the article isn't specific about how people were recruited for this one. There isn't enough information to tell how much skew might have been introduced as a result. Surveys are always kind of iffy as information sources: not meaningless, but with a lot of subtle noise in the signal.
Does it though? I'd think you'd probably want at a minimum, n = 100,000 to have any sort of representative sample. I don't think it's a stretch to surmise that there are at least, what...a hundred million anime fans in one capacity or another, worldwide? Anything much less than 0.1% of the actual population is susceptible to some major deviation from population-wide statistics.
That isn't that many people. This is like 0.04% of the people subscribed to the r/anime subreddit. and just 2.5% of the number of visitors of an anime convention in my country.