I can't imagine you'd get anywhere with a delay reclaim for that, 2 minutes early would just be put down to you not allowing enough time if you missed it.
You're probably right but I don't see how this view is legitimate.
If they say doors may shut 40 seconds before departure I don't see how they can reasonably say "Oh well actually we shut them more than 2 minutes early but really you shouldn't have expected us to actually do something as difficult as waiting for the correct departure time and it's your fault for not getting there earlier".
Should trains ever leave early? No?
Will mistakes happen? Yes
Should the passenger be blamed in such circumstances? Not in my opinion.
If I missed a train because this happened I'd certainly push a claim as far as I could.
I've lived somewhere that I commuted from a station a few minutes walk away. I knew how long it took to get there. I usually cut it fine, getting to the platform 1 or 2 minutes before the doors shut. If the train had left early (it never did) I don't see what that should be mine and not the railway's problem.
(Not that Delay Repay would have got me much...)