A star usually is larger than its planet (one might get different results for bodies orbiting stellar remanents like neutron stars or for hot jupiters around a very low-mass red dwarf), and that's what they refer to in this instance.
Further in the text they explain that they mean the star eclipsing the planet:
An eclipse occurs when an exoplanet passes behind its star as seen from Earth, and a transit occurs when a planet passes in front of its star.
(emphasis mine)
And this of course means that the star blocks any light coming from the planet, not vice versa. The information gained from this measurement where the star eclipses the planet is that it allows us to compare the spectrum of the star compared to the combined spectrum of star and planet, allowing possibly some deduction on the atmospheric or chemical composition of the latter (similar to the transit).
HOWEVER: If you consider a hot jupiter (thus a gasous planet very close-in) it is thinkable that it might occur that a planet is bigger in diameter than its host star. This planet would have to orbit its host star, a low-mass red dwarf, very close in. Then radii might be of similar size to an extend that the planet might even be larger (yet still not more massive) than the star itself. A hot jupiter can reach about twice the size of Jupiter - and low mass stars at the lower limit of about 0.08 solar masses have sizes comparable to Jupiter ($0.1r_{Sun} \approx 70.000\mathrm{km} \approx r_{Jup}$).
If you consider neutron stars (pulsars), the first dectections of exoplanets were even around one of those (though technically... are they still planets, if the central object does not show fusion anymore?).