Indeed, the properties of this filament are kept rather secret, so to find out what the density is, you need to either contact the filament supplier or the manufacturer for accessing the data sheet or calculate this yourself. The answer below expands on the "calculate it yourself".
Density is defined as $\rho = \frac{m}{V}=\frac{[kg]}{[m^3]}$. The use of this formula has been show in this answer. The drawback of that answer is that it is an approximation that relies on a uniform piece of filament that requires cutting off expensive filament and relies on assumptions rather than actual calculations. Furthermore, the weighing of a small piece of filament is much less accurate of a small piece than for a larger piece or the whole spool (for the same scale, so a decent kitchen scale might be usable when more weight is concerned). You could improve the density calculation by measuring the diameter at various sections and make a better approximation based on the average diameter, but still that would need you to unroll the spool and carefully measure a piece of filament (and cut it). The advantage of that answer is that it is far easier than my proposition.
The method that is proposed here relies on a well known method to calculate the density of materials that is called hydrostatic weighing. Hydrostatic weighing uses the displacement of a fluid due to a submerged object to determine the density of the object. Any submerged object will displace the fluid surrounding it by it's own volume, as such you would need to measure the rise of the volume level to read the volume of the submerged product. This can be done accurately by using methods that include containers of known dimensions, known fluids and even an overflow method and weighing.
If the filament comes on a spool, you would require an identical spool to prevent removing it from the spool. But, I read that it is sold in bundles, not on spools. Without a spool would make it even easier to calculate the density as you do not have to subtract the spool weight and volume, the answer continues as if you have it on a spool. This is purely necessary so that you would not need to cut off filament or unroll the whole spool. The suggestion below let's you measure the whole spool, so weight is measured more easily as there is a lot more.
Theoretically, you could put the filament in a fluid which is known to not affect the filament properties (so not water for GEL-LAY!) in a bath of known dimensions. Once the spool and filament are completely submerged, you could measure the volume rise. If you do the same for the empty spool, you also know the volume of the spool alone. If you also are able to weigh the empty spool and the full spool (before you plunged them in the "bathtub"/container), you now know the volume and the weight of the filament, dividing the weight (full spool weight minus empty spool weight) by the volume (full spool submerged volume minus empty spool submerged volume) will give you the density.
$$\rho_{filament} = \frac{(m_{full\ spool}-m_{empty\ spool})}{(V_{full\ spool}-V_{empty\ spool})}$$
Now let your filament dry for a long, long time! :)