That chart also includes the EIA's figures for crude and condensate (C&C), a narrower definition of oil that excludes biofuels and natural gas liquids that are debatable as to whether or not one wants to consider them in oil supply trends. Global C&C production has been almost flat since 2005 - a bumpy plateau that slopes only very slightly upward.
picture shows the various oil production series, together with Brent oil prices (inflation adjusted, on the right scale).