As you say, the contrast between seeing (star + planet) during a transit, versus star alone, is enough to identify absorption of infrared light by some chemical species.
The simulations in the above paper basically show they can infer some chemical abundances (carbon, oxygen) and some atmospheric parameters (inversion layers) for Neptunes and Jupiters. But probably not for Earths, so not for the system in the OP. Even for big, thick atmospheres, these spectroscopic characterizations take a lot of observation time (like, days).
The race is indeed on to develop instruments and algorithms for this problem -- e.g., detecting CH4 or CO2 in an exo-Earth atmosphere. There's feverish activity in the Astronomy community around this, and post-JWST missions are being formulated to tackle the problem.
The concept you link is a "starshade". It's a sister concept to a "coronagraph" -- both use an occulting disk to block out the light from the host star, so that a non-transiting exoplanet can be observed.
One goal is to image exoplanets directly, and another is to gather spectra for characterization. One of two current mission studies doing studies of the two approaches is HabEx (http://www.jpl.nasa.gov/habex/). Obviously, the starshade is more complex/cumbersome/expensive.
Using one method or another, you have to achieve a contrast of about 1e10 between the star and the exoplanet. For every 1e10 photons that come in from the host star, your starshade/coronagraph has to let at most one get through to the detector.