Avanti's Passengers' Charter says:
We offer compensation after 15 minutes’ delay, no matter what caused it. The longer you’re delayed, the more you can claim up to the full cost of your journey with us. You can see how it works below. Compensation is based on the time you arrive at your destination station [...]
I would argue there is a distinction to be drawn between the time the train arrives at your destination station and the time
you arrive at your destination station. Normally there would be no significant difference, but there is if they fail to open the doors for 8 minutes. Compensation is, according to the contract, based on the latter, as stated above in the Passengers' Charter.
The trouble is, they're looking at the industry data and taking the train's arrival time to be an accurate reflection of when you arrived. As such I'm not the least bit surprised your claim was rejected. It's one that needs to go via Customer Relations.
In order to persuade them your arrival at the station was delayed after the train pulled into the platform, it would help if you had evidence. For example, filming yourself exiting the train as soon as the doors were released, then getting footage of the station clock once you've disembarked, could help establish what time it was when the doors were released.
Failing that, I suppose you could put in a SAR seeking CCTV footage of yourself arriving at the station, however, they can charge a fee for responding to a SAR which might be more than the delay repay at stake. You could also speak to their Customer Relations explaining when and where this happened, and asking them to check with the station manager who may be able to verify the fault with the doors on your train.
I must say, if they're not going to compensate passengers who wait patiently and are delayed during these frustrating events, they will be lucky if people don't take the message from this that they should just pull the emergency door release and avoid the delay in the first place.