The association of ellipses with cue sports dates at least as far back as 1885, the year that the comic opera The Mikado by Gilbert and Sullivan premiered in London.
The Mikado is Gilbert and Sullivan's most famous work and is one of the most performed pieces of musical theatre in history.
The song A More Humane Mikado mentions "elliptical billiard balls". It's in the clip above at 6.22 minutes - it's worth a watch just to see the terrific enunciation of the word "balls".
The full verse is as follows:
The advertising quack who wearies
With tales of countless cures,
His teeth, I’ve enacted,
Shall all be extracted
By terrified amateurs.
The music-hall singer attends a series
Of masses and fugues and ‘ops’
By Bach, interwoven
With Spohr and Beethoven,
At classical Monday Pops.
The billiard-sharp whom anyone catches
His doom’s extremely hard—
He’s made to dwell
In a dungeon cell
On a spot that’s always barred.
And there he plays extravagant matches
In fitless finger-stalls,
On a cloth untrue
With a twisted cue
And elliptical billiard balls.