No, it isn't irrelevant - it is there to set up the Doctor's emotional context. As a context, it has to make sense.
In addition, for the audience, it was called a "Time War", but the only elements we see look pretty much like conventional war. There's nothing Time-like about it. It's just a war, like other wars. They set an expectation that this war was special, and then failed to live up to that expectation, which isn't good storytelling.
All of which, as noted, could be handled with a couple of sentences, which is the sad part. This could just be an editing failure - the bit we need may be on the cutting room floor.
