Doom of Valyria - A Wiki of Ice and Fire (westeros.org)
The details are vague, but it wasn't a dragon vs. dragon thing. The real-world inspiration seems to be Atlantis, the thematic inspiration is "the Valyrians were gits, so karma bit them in the backside."
That's underselling it. Daenerys had three dragons. She lost one to the Night King (who is no ordinary man, and only downed Viserion through supernatural ability) and lost another to a ballista, which was specifically designed to counter the dragons, and despite all the ballistae that were produced, Rhaegal was the only one who was downed, and only then through a combination of circumstances.
If anything, it reinforces just how powerful dragons are, given how limited the ballistae were against them. Yes, Rhaegal was killed, but Drogon alone was enough to take King's Landing.