It didn't happen that way-

In November of 1993, UFC I took place. I was recently re-watching some of the action when something curious came up. Another video on the side featuring participant Ken Shamrock was advertised, and so I watched that video.

In the video, Ken Shamrock claimed that Royce Gracie choked him with the gi - a sleeve choke called "sode-guruma jime" in Judo. Though sode guruma jime would have been perfectly legal under the rules of the UFC at the time, Shamrock likens the use of the gi to choke him as being unfair since he couldn't wear shoes (shoes were seen as a potential weapon).

In reality, Gracie choked Shamrock with a rear naked choke (RNC), also known as hadaka jime.

In the UFC match, the camera angles are not perfect, and some of the action can be hard to see - especially for an untrained eye. However, I saw it immediately, as did others. Interestingly enough, Bill Wallace, commentator, immediately spotted the hadaka jime. Wallace, a black belt in multiple disciplines, including Judo (which uses hadaka jime), observed correctly.

Interestingly, Wikipedia lists the victory for Gracie as being via RNC.
Sherdog also lists the submission as RNC.
So does this source.
In fact, I could not find anybody not associated with Shamrock who says the win was via the sleeve choke - sode guruma jime.

Here is a nice breakdown by Rener and Ryron Gracie on how the entire fight played out.