The thing about trying to describe chipmusic in a paragraph or so is that it's ultimately doomed to fail if you're trying to explain more than the surface of it. Although anybody who's been into it for long enough clearly understands all the nuances by sheer force of exposition, it's not easy to put into few words.
For example, for me chipmusic is an esthetic choice. I don't give much thought to what tools were used to create the music, as long as you respect a few loose "rules" about the sound. For others, it's strictly a choice of tools. Some think that sample trackers aren't chipmusic because there's no actual sound chip involved etc. Then there's the whole crossover thing where a lot of people use chipmusic as an instrument rather than a genre. You'll get chip-rock, chip-house, and etc etc. Some people call it 8bit music even though the (very) large majority of platforms used to make chipmusic isn't 8bit. Some people try to sound like videogames, some like the demoscene, some stay away as much as possible from this and try to make "modern" music on old hardware... some make "old" music on modern hardware.
In short.. it's a fucking mess. But it's not very confusing when you get familiar with it. The scene is usually both very elitist and very loose about what qualifies as chipmusic. Contradictory? It sure is.
When I say your description is "wrong" it's mostly because you state clearly that chiptune is something that doesn't use samples. The "official birthplace" of chipmusic is the Amiga, a computer that didn't generate any real time sound and relied strictly on samples. The term "chiptune" was invented in that era because they were "tunes that sound like old sound chips". One can argue that the C64 which came before was chipmusic too, and you'd be both right and wrong. Right in the sense that.. by today's standards and definition, all the pre-amiga soundchip-based platforms are seen as very valid chip machines. But wrong in the sense that back then.. it wasn't called chiptunes, it was just called music...or computer music... or noise, by the parents being subjected to it.
In a sense.. it's like any other genre of music. Since music is an ever changing, very organic and living thing.. new genres generally just don't happen overnight. They are a result of years of permutation and kinky interracial sex between other genres. Nobody knows exactly when rock n roll became rock n roll. It was a result of RnB being pushed outside of its standards, Of blues being played "wrong". Of country/western being played too hard etc etc. But for simplcity's sake, people generally tend to agree on a starting point/era, even though it's almost meaningless since all that came before it shares tons of similarities. In the case of chiptunes, the accepted birthplace is the Amiga where the term was coined and the genre refined into something identifiable. And in those days, we used only samples. Super short samples, often a single cycle, but samples nonetheless.
I find myself constantly changing the way I refer to chipmusic or try to explain it depending on my audience. For some of my friends.. I can say "chipmusic" and they know instantly what I'm talking about. For others.. I have to call it "my nintendo music" otherwise they don't get it. If you're trying to explain it in a single paragraph for people who have never heard it before, don't give specifics about the technical aspects of it like "it has no samples" or "it's from sound chips" because you'll always get nitpickers, like me, to point out it's not quite right 
"Chipmusic is a forward-facing and ever evolving genre of music deeply rooted in the early digital computer music of the 80s"
Or something like that... yknow.. keep it simple and surfacey, otherwise you'll end up saying something that's not true
.... damn that was a uselessly long post.
