Some languages in 1Ed could be interpreted to work this way. There were root languages and dialects. Elvis and Giant are root languages. Drow, Wood Elf, Grey Elf etc were dialects of elvish. Fire Giant, Ogre, Hill Giant etc were dialects of giant.
Historically speaking, this is actually fairly correct, at least in Europe (that I know a bit about). It is said that a language is a dialect with an army, and that rings true to me. The modern monolithic languages like English, French, Italian, Spanish, and German started as a collection of dialects melding into each other. Depending on how many languages you want in your world, all these could be divided into two (Germanic and Roman), you could use the modern languages I named, or you could have maybe 25 major dialects, all with their own names and vocabularies.
On top of these, of course, we have the small languages that belong to their own families, like Welsh, Räto-Romanish, Basque, and Breton. I heard someone say that the Amazonas contains more language families than any other part of the world - two tribes living as neighbors can have languages as different as English and Chinese.
Just an example: Allemaniac is a mix of German and French spoken in Alsace-Lorraine (Or Elsass-Lothringen in German). It is neither German nor French, but sufficiently similar to each that both French and German nationalists have claimed the area (it changed hands a couple of times over the centuries). I quoted it to show that there will always be border cases; just as this is neither French or German, it is neither Germanic nor Roman.
Another example: Scandinavia was never politically unified, and now has 5 different languages that are slowly drifting apart, dialects merging into languages that are being unified each in their own mold, very much thanks to TV.
A third example: Back in school, there used to be students receiving education in Serbocroatian because ti was their parents' language of origin. Today, this is two languages, Serb and Croat. As far as I know, the major difference is that there is now a border between the speakers of each.
Conclusion? Basically, you can handle languages any way you want, and no-one can really fault you. Just select your own level of abstraction.