This is a case of the chart telling a different story from the data. Let's look at one of the charts, piece by piece.
What is the whole? It's hard to interpret without some explanation. The title at the bottom says "Radiative Forcing change over the last 30 years" with a footnote disclosing... hold your breath... "Radiative forcings from other gases and human impact are not shown."
This pair tells a particular story: Methane was a much larger share of something in the past and is predicted to become an almost irrelevant share of something in the future.
But such an interpretation would almost surely be wrong. The designer left a misleading cue here, which is to show two pies of equal size. There is just no conceivable way that the total "radiative forcing change" is identical in the last 30 years to that in the next 30 years.
The second pie chart also has a footnote. A better person can help me interpret what the following sentence means:
The radiative forcing that our current emissions have committed us to, 20 years from now, is based on a 300-year initial drawdown time scale for carbon dioxide, and 12 years for methane
I'm sure these words say something to a climate expert but this attempt stinks as a piece of public communication.
Returning to the equal-size pies for a moment. Since all other factors are removed, the chart only shows us the relative impact of Methane versus Carbon dioxide. If the data are to be believed, then the scale of the impact of Methane is expected to become much smaller relative to that of CO2 in the next 30 years. This does not imply that the absolute impact of Methane will be lower in the future than in the past.
There are three possible stories, all consistent with the above chart:
1) the absolute impact of Methane declines while the absolute impact of CO2 increases, and thus the relative impact of Methane decreases drastically
2) the absolute impacts of both decline but the impact of Methane declines a lot more
3) the absolute impacts of both increase but the increase of Methane's impact grows a lot more slowly
It is the designer's job to make it clear to readers the story of the data.
The fact that the entire blog post contains a PDF image and no words is either laziness or arrogance. The title of the piece is "the story of methane, in five pie charts". I don't know what the story of methane is. I doubt that the intention of the author was to tell us that methane is extremely unimportant relative to CO2.
PS. Steven below linked to a response from RealClimate.org. They confirm that the "story of methane" is that it is unimportant relative to CO2. Perhaps they should have called it the "non-story of methane". They see no problem with these pie charts.