Slightly off-topic so I'll make it brief:
(I am scratching my head about the ultimate source of this very-deep gas source; it seems too deep to have come from rotting dinosaur carcasses. And a parallel question is - where did all the methane on the planetary giants in our solar system originate?)
Not just rotting dinosaurs - rotting
anything that ever lived: trees, ferns, microbes, plankton, you name it.
Shells are calcium
carbonates, and collecting on the bottom of the seas (for several billion years), form sedimentary rocks like limestone, marble, and the UK's famous chalk. Which get subducted under (slide beneath) other rock layers along ocean-rim fault lines.
On other planets with no known bio-sources - a good question. But the Universe was around for 8 billion years before the solar system formed. The "dust" the solar system was made from likely contained a lot of "pre-owned" crud from older star systems.
Methane is a pretty simple compound - process one carbon atom together with two H2 molecules (most common element in the universe), and it's "methane party" time.