I don't speak Japanese, so I had some questions about whether this was intentionally or non-intentionally silly. Cross-cultural expert Lisa Katayama came to my aid. After checking out the preview, she emailed me to say that it is definitely a parody:
The intro text says, roughly: if there are only two kinds of movies in the world, monster movies and non-monster movies, then director Hayashi likes monster movies much much better. And then each character is introduced by their stereotype: the heroine who wants to become a teen idol, the reliable mom-like older sister, the naughty little sister... and so on.
Good to know that Hayashi realizes that there are only two kinds of movies in the world. And that he understands giant monsters always beat non-giant monsters in any cinematic smackdown.
Quiet Earth, the post-apocalyptic funhouse that first brought this movie to my attention, gives a more straightforward summary:
Set 60 years after the original (Deep Sea Monster Reigo), in modern-day Tokyo. Global warming causes the southern polar ice cap to gradually melt, disrupting the ecosystem and luring ancient sea monsters to Japan. Eventually an enormous sea beast called Raiga enters Asakusa via the Sumida River and begins wreaking havoc on the buildings there.