Alright I'll be short with this since you clearly don't understand basic human interactions.
First of all, you're clearly making fun of him by the way you're speaking to him in voice in that recording.
That instantaneously throws your admin abuse claim out of question based on the fact you are knowingly being a douche about the situation.
I would also like to point out that in the rules, it does state that admins can use their own discretion in certain decisions and it looks like you're upset someone won one over on you.
I'll leave these chat entries for laughs here by the way!
Welcome to our gay ass website
08-30-18 01:36:41 CS:GO Surf im not going to ur gay ass website
08-30-18 01:36:58 CS:GO Surf are u retarded
08-30-18 01:37:18 CS:GO Surf suck my balls faggot
You really sound like you want that ban removal but I'll go with a denial on this one.
The ban is only one day so I'd argue your best move is to move on and stop being a child.