Not millenia. The oldest novel that we still read is The Tale of Genji, written in 1010, followed by Romance of the Three Kingdoms, followed by Don Quixote. That's three still-relevant novels from 1010 to 1605. There are assuredly dozens to hundreds of novels written in that time period. Three are still relevant today.
Whereas many ancient Greek and Roman plays are still performed today, right alongside Shakespeare. The play is simply a more durable form of literature.
Wikipedia describes Lucian's True Story as a novel written circa 200 AD. I had to read it in high school. I'm sure there are other examples.
On other comments you describe Quixote as one of the first novels ever written, not just still read, which is definitely very, very far from the case. Don quixote itself cites legions of prior novels!
Apuleius' "Metamorphoses" is probably the oldest complete novel known. It is from the second century, so much older than the novels you mention. And it is still read - at least I read it a few years ago in translation and found it hilarious and fascinating.
Whereas many ancient Greek and Roman plays are still performed today, right alongside Shakespeare. The play is simply a more durable form of literature.