As mentioned before - Red Gyarados was put in to tell players that now they could even find different-coloured versions of their Pokemon, with a cool shiny effect and also guaranteed decent stats to boot - well, for those who knew leastways, I think (apparently all Pokemon in 2nd gen games ran on a different IV systems which was what determined whether a Pokemon was shiny). They also told players other Pokemon could be shiny (such as an NPC talking about seeing a shiny (pink?) Butterfree, and the 'Odd Egg' in Crystal which had a 50% chance of being shiny).
Was it necessary to do this - no, not really - but also as mentioned, then people would be going on about their shiny Pokemon, which would for a while have been regarded as false, just like the good, old Mew-under-a-truck/get-a-Pikablue/get-a-Yoshi in a Pokemon game rumors (except for the few who believed those, which is easy enough if you're young and all I suppose). In that regard I think they would have 'needed it' then.
For the storyline; it adds something as well, I suppose. After all, given TR's forceful evolution of Pokemon and all, a Gyarados - which is impressive compared to Magikarp but died to electric attacks, and could be found by fishing - doesn't quite measure up to a Red, shiny Gyarados (I'm ignoring the stuff from the anime about it possible having always been that colour and the red is a side affect as in the game it's shiny IMO, and games =/= anime). It does add that extra bit to it, which is certainly enough for children playing it. Was for me leastways. :P
But for this discussion on whether it really is a shiny or not... well, IMHO, it's a shiny Pokemon, as I take shiny Pokemon to be ones who have a different colour, and in the case of GSC ones - a Pokemon that also comes with certain IVs going by game mechanics. Sure - it's a given that it is a shiny Pokemon, but it still is a shiny Pokemon to me - just an easy one to get. Even though I referred to it as the Red shiny Gyarados...
After all; in D/P/Pt, you can get shiny Pokemon in an easier fashion thanks to chaining (and never mind the fact you can also trade for one with Wi-Fi), and in GSC, you could actually breed for one if you knew that you could (again - certain IVs make a Pokemon shiny - one 'shiny' parent led to... a 1-in-256 chance, and 2 shiny parents a mere 1-in-64 chance of the offspring being shiny IIRC).
Looking at this question from the point of view of the child I was when I played Silver though - I'd wonder why people think it unnecessary when we were talking about a _Red shiny Gyarados_ here. XD