is that fair?

[Giordano Bruno 1974]

Do you honestly think I'm wrong though?

Wrong to be skeptical? No.
Wrong to seemingly suggest that OP was deserving of it? Yes.

I doubt the provided logs are fabricated. It appears OP tried to kick pirdim from the table for exceeding their time; which then elicited the response in the logs.

I do not know what went on because no context is provided. There are chat logs of the one player only. I think it is unlikely that nobody else wrote anything, least of all the original poster.

I think it would be highly unlikely that the original poster did nothing wrong and got punished by a mod. I don't get that vibe from this site. I also had a quick look at the original posters' profile and there are a lot of delay of game penalties and a few ragequits. Therefore I think s/he is being disingenous about what really happened. That makes me think that it was fair.

Now I can be wrong but I don't think I'm being unfair as I was asked for my view and I can only go on the information that was provided and that which I can readily find. You might be right about the red thumb in which case it is possible that other players gave him / her red thumbs for little cause but as the original poster didn't talk about that I'm not going to speculate about whether that would be fair or not.

[N_Faker]

I think it would be highly unlikely that the original poster did nothing wrong and got punished by a mod.

Neither have been moderated with any penalty.

None of the quits are ragequits, all of the three games still on the list are 'out of time' kicks. One of them by pirdim.
'Out of time' marks are also exceedingly common for TTA due to the highly varying number of turn actions, especially when undo is used.