Hi Rok - first of all, "mellophonium" is actually a strange name. Perhaps Conn called their instrument by that name as a marketing thing. Usually, the instrument is referred to as a "mellophone." They are still very much in use in marching bands all over the country. What that article means is that Conn does not make one any more. There are plenty of other makers of mellophones, unfortunately.
Basically, a mellophone is most similar to a trumpet, except it is in a lower key, more similar to the range of the French horn. So in jazz, like in Stan Kenton's band, they were played by trumpet players. This is actually what the instrument was invented for - a "mellower" instrument that a jazz trumpet player could use. Think of it as an alternative to the flugelhorn, except the flugle horn became much more popular with the trumpet players. My guess would be that it was actually a trumpet player in your article, since he was part of a jazz group, I think you said?
However, in high school and college marching bands everywhere, there is always a mouthpiece extension fitted to the mellophones, so that French horn players can play them with their French horn mouthpieces, instead of the trumpet players. I had to play one of those things for two years in a high school marching band, and hated every minute of it. They are poorly designed instruments that do not play very well in tune, and don't have a particularly interesting tone quality. They are used by the French horn players in marching bands because they are bell front instruments - as you know, the French horn bell faces backwards, and it is much easier to march and play a mellophone than a French horn.
Another key difference is that mellophones are cylindrical instruments, like the trumpet (like I said, they are basically big fat trumpets) and trombone, as opposed to conical, like the French horn and the tuba. This accounts for the brighter tone quality, closer to a trumpet in sound than a French horn is.
I have had to play some of those Stan Kenton charts in the past on pops concerts, though of course we played them on French horn, which made them much harder, since they were definitely written for trumpet players playing mellophones - they are very high parts, and though I made it through that week, I actually injured myself doing it - the first time that had ever happened to me in my career. I hope I never have to play them again.....I should explain that my specialty on the horn is the low register - I play the bottom part in the section, I am the bass of the quartet of horns, if you will. So those screaming high Stan Kenton mellophone parts were especially difficult for me personally. If you go on YouTube and look for videos of the Stan Kenton band, you can see the difference between the trumpet and the quite a bit larger mellophone. They are trumpet players playing them there. It is much more common in marching bands for horn players to play them, though, and that is about the only place you ever hear mellophones anymore. They suck, and just about all horn players hate them with a passion. They also confuse the kids, because since they are actually big fat trumpets, they are fingered like trumpets, instead of like the French horn. So the students have to use one set of fingerings in marching season, and another set when they go back to their French horns for concert season.
I believe you live in Texas somewhere? If so, you have definitely seen mellophones at pretty much any high school or college football game on the marching field at halftime. And it is definitely the poor horn players that are forced to play them, sigh....my junior year, I escaped to finish high school at an arts academy, and never had to play one of those damn things ever again. Never had to play in a marching band ever again, either. That is terrible for the embouchure - it ruins many, many brass players.