Since you say that you received a 14 day ban recently, we can conclude that your permanent ban was not because of only 1 game.
To start, the punishment system currently works in tiers, as follows:
1.) 10 game chat restriction
2.) 25 game chat restriction
3.) 14 day ban
4.) Permanent ban
The punishment you receive is based off of recidivism, meaning that each time you are punished, you will move up one tier in the ladder, regardless of how "minor" the offense may have been. It is possible to skip tiers if Riot determines your behavior to be particularly extreme, though this is rare.
Since you had a 14 day ban recently, this means that, because of how the system works, your next punishment (this one) would be a permanent ban, and it was. Permanent bans are not solely based on the severity of an offense, they are also given based on frequency. Anything minor offense that would give you a 10 game cat restriction will give you a permanent ban if you do it frequently enough. So really, when looking at chat logs, they're mainly looking at if the chat logs are deserving of a punishment, and if they are, you will receive a punishment based on your history with the system.
All of this means that your permanent ban was not based solely off of one game. It was due to that game as well as all the other games that got you your previous punishments as well. You essentially showed Riot that you have no intention of changing your behavior, so they permanently banned the account.
As a side note, receiving only one game of chat logs in your e-mail/client does not necessarily mean that it was the only game the caused the punishment. The system is designed to send you 1-3 of the more recent matches, but it's not necessarily a full list of everything you did wrong that lead to the punishment.
EDIT:
I really feel like what should have been done is I get a direct warning saying that if I'm toxic anymore I'll get permanently banned
In the e-mail you received for your 14 day ban, it should say that your next punishment will be a permanent ban.