On Earth, where we know there is life, the default source of all hydrocarbons is life-related. There are inorganic routes to produce methane, but the volume produced is not likely to be high, and also is unlikely to be trapped in the rock. Even deep hydrocarbons (the ones the original AC is talking about) are probably formed by microbes living in the rock at depth. Shale gas is formed directly from biogenic organic matter in the shale - shale usually has a high organic content, so much so that some shales in the UK are used for brick making because the organic content is high enough to require little additional fuel. Indeed, shales are likely source rocks for hydrocarbon deposits! The organic content in all these cases is biogenic.
The point of Martian methane is that if it isn't associated with volcanic structures, it is a pretty good smoking gun for biological processes here and now, not millions of years ago.