Derrin Brown often lies about how his tricks are performed... it's part of his misdirection.
Still - that could be one way. I've seen Derrin prime people to draw the letter A for example.
But the tricks are never failed. That means you are saying for video this trick is okay but if we perform live it would be busted in end by the volunteer saying " I did not drew anything."
Whole trick then flops for audience.
This magician is even selling his trick in a kit, which means there might be some secret stuff in cards or blindfold?
Yes I am not beleiving in ESP here but trying to find out a genuine logic for this trick.
... well to know for sure what the genuine logic of this trick is, you should find someone who has purchased the kit and ask them. All we can do is make educated guesses about how the trick could have been done.
You are correct: the fact there is a kit suggests that there is something about the cards ... a trick deck so the sender always gets a particular card and a marker pen that does not write would be my guesses (+ instructions) since those are the key props.
Note: the person set up in a trick like this seldom outs the magician very publically: that would be "being a bad sport" (Dynamo often relies on celebrities wanting to look good on TV ferinstance) ... but the magician does not have to rely on that.
The receiver in this trick never gets a chance to say anything to the whole audience at once: he does not get the microphone, he remains blind at the reveal, and gets whisked off stage as soon as the trick is done. He may tell everyone close by, once he's back in the audience, that the pic is not what he drew ... but few of the audience will hear that and a bigger production could whist the volunteers off backstage insread (to enjoy promotional treats or something - you can figure this out).
But let's say a receiver manages to get to the mic and call out "hey that's not what I drew?" The magician can simply invte the audience to doubt his word ... "clearly you did: how do you know, you were blindfolded" etc.
So it is unusual that someone will; be able to spoil the trick in the way described. In that rare case, do you think that the video of that performance would be edited into a promotional video? The video we have only shows tricks that worked - we do not see video of any of the tricks that don't work ... and the magician says in the clip that it does not always work: the receiver pic is not always as good a match as the ones in the video. This process is called "cherry picking" and it is common in advertising and pseudoscience.
Seriously - I should not have to do all this work for you.
I have outlined very common approaches to this sort of trick that have been used many times by myself and other magicians through history.
I suggest you invest in a book on magic or look up the many "how this trick was done" videos online to see how similar tricks get done. Start with the simple ones and build up: there are no original tricks - they are all variations and combinations of existing ones.
You should also study the techniques of skeptical inquirey and read up on common pseudoscience and charlatan debunking.
We'd like to think that we are not easily fooled but tricks are usually embarrassingly simple once revealed.