A gas giant is not just a failed star (i.e. an object with the same composition as a star, but that can't gather enough material to achieve fusion), it's formed differently from a star. A star forms from a diffuse molecular cloud collapsing on itself. You can have a binary star system when that molecular cloud is fragmented enough, and so you end up with two stars forming from the two main fragments, where both stars are born roughly at the same time and following the same process.

There could be a scenario where the second fragment is just not massive enough to achieve fusion, which is what you are alluding to, in that case the second fragment could give birth to a sub-brown dwarf [1].

A gas giant has a different composition from a sub-brown dwarf though, because they form differently. A gas giant is formed after the star, not at the same time. First the star forms, and the leftover material around the star starts clumping together in orbit around it, this allows the formation of a rocky core and at some point if the core gets big enough it starts the runaway process of pulling more and more gases, creating a gas giant. So a gas giant would have a higher density than a star of the same radius, because the massive rocky core is there. This was thought not to be a possible scenario around a small star, as we didn't expect a small star to have enough material left in it's orbit to allow the creation of a core big enough to start the runaway gas accumulation necessary for a gas giant.

Here, based on the mass/radius/temperature of the object, they were able to infer that it must have a core of roughly 12±2 Earth masses of dense material. Hence it's a gas giant (formed around a core, and thus after the star formation) and not a sub-brown dwarf in a binary system (formed at the same time as the star).

Obligatory disclaimer that I'm not an astronomer, just a hobbyist in the field.

[1]: https://en.wikipedia.org/wiki/Sub-brown_dwarf