Yeah, it's a little unclear but I think your interpretation is correct. The key is the paragraph beginning with:
> Imagine my surprise: according to the duly signed option agreement, my options were meant to vest over four quarters, not four years, as both NVIDIA’s CFO and their outside counsel, Cooley, had asserted back in 1996.
On first reading it did give me pause because it's the first time "four years" is mentioned. But on another scan I agree it's cleverly written and never actually claims the agreement was four quarters, only that the paperwork says that.
Still it is a funny story, similar to those "I spent 20 Bitcoins on a pizza" ones, I guess.
“Imagine my surprise” seems really damning. A contract is supposed to be a meeting of the minds. The two sides agree on what the contract means and the written artifact is a record of it. If he’s surprised then that suggests he never intended it to be quarterly. And clearly the other party never meant that either. I’m no lawyer, but I don’t imagine “I didn’t mean this and they didn’t mean it but that’s what got written down so give me money” would fly in court.
I still don't think I understand the actual events. Is it that he got 1/4 of the shares as he expected after a year and did not chase for years 2/3/4 (and they never offered them)?
They should just offer to settle at a reasonable value as if it had been just the four quarters previously agreed, but a smart decision was made to sit on the shares.
There are documents linked in the footnotes that spell this explicitly, you don’t have to infer this:
The offer letter, which spells out “which vests over 4 years”: https://colo.to/invitation.pdf
The option grant which has the accelerated schedule: https://colo.to/grant.pdf