As I found out not too long ago, that debate was already mostly settled when I learned it and is long-settled now -- gas giants have a icy-rocky planetary core formed in the accretion disk along with the other rocky planets, and the much larger mass that they build up allows them to hold an enormous atmosphere during accretion while the rocky planets will bleed or evaporate most or all of theirs away. (See perhaps NASA's brief on planet formation -- I feel like Wikipedia's article is skirting the gas giant issue so probably has some conflict between editors.)

A failed star is a brown dwarf, which can form as part of a binary just like any stellar binary. The reason this particular system isn't that is that they say it's specifically a Jupiter-like gas giant. Further, they obviously got the mass since afaik methods of finding exoplanets will always get the orbit (by wobble at least), and the article says recorded the light during transit, so they would have calculated the radius; thus they'd be able to calculate the planet's density. Now, the density of Jupiter is 1.33 g/cm^3. Compare a brown dwarf, which as a failed star has no (or very little) core fusion to provide pressure that counteracts the enormous compression that's from the gravity of its enormous mass (about .07 solar masses, which is still huge) -- it is thus degenerate matter (in the core at least), as in a white dwarf, and at least in one case the average density was calculated at 108 g/cm^3. There would be plenty of other evidence to line up too -- I'm sure they weighed the possibility that it could be a brown dwarf, or at the very least a very unusual type of planet that must be tested for everything.

(And just for fun, the densities of main-sequence and off-sequence stars are all "known" (more or less -- it's not pure hydrogen or pure clean fusion), because math. I can't find a simple list, but you can find masses and radii -- anyway, as a type-M star, it is about 5 g/cm^3; compare the Sun at about 1.4 g/cm^3 -- more mass means more pressure inward, but also more fusion so more pressure outward,(See Thompson, Astr 1144 Lect.10, OSU)