För mig som har pluggade svenska för över 6 år det rätt ordet är DEN. This seems wrong, since when you're using en words then it is DEN instead of det. Please do correct me if I'm wrong, but this is what I've been taught over the past 6 years in school. Futhermore, in the spoken slowmotion sentence the voice says DEN. In spoken language these -n and -t sounds are being mostly silent.
There isn't much sense behind the genders. Historically, it's called common gender because we used to have three genders, feminine, masculine and neuter, and the first two melted together into common gender. There are some tendencies, for instance words with the ending -ing are typically en words. (except the word ett ting 'a thing', where -ing isn't an ending).
Some more about these tendencies here: https://www.duolingo.com/comment/6329293