It tells us that according to Dr Katy Sheen, a physicist in the geography department of Exeter University, it would all work if Father Christmas travelled at 6 million miles per hour. This would get him around the world in time, and, as a bonus, (enter Einstein) 'drawing on Einstein's special theory of relativity' Dr Sheen worked out that he would shrink in the direction of travel, and 'at Santa's speed the shrinkage in so extreme he will appear invisible.'
Leaving aside whether or not 'appear invisible' is oxymoronic, there are two issues here. First let's assume Dr Sheen is right, and the relativistic contraction is significant. This would also mean that time dilation would be significant. So by the time he got round everyone, there might be issues with him having moved well into the Earth's future.
However, in practice that isn't a problem, because the shrinkage argument falls apart. If it's literally true, it doesn't help because, as the newspaper article pointed out (but Chris Evans didn't) the shrinkage is only in the direction of travel - he'd be as wide as ever sideways. But just how big would the effect be at 6 million miles an hour? It certainly sounds very fast. It's around 9.66 million kilometres per hour, which is 2.69 million metres per second. Fast or what? But the speed of light is around 299.8 million metres per second. So Father Christmas is only travelling at 0.008c.
The formula for the contraction is not complex. It's the original length x square root (1-v2/c2).
So that makes Santa's new front-to-back size 99.99% of what it was before. Not very helpful. Given the relative closeness of 269 to 299, I do wonder if the intention was for him to be 100 times faster - but every newspaper story I can find uses the low number (I couldn't find the original press release).
Am I breaking a butterfly on the wheel? Probably. But there would have been nothing wrong with giving a more realistic velocity. I've got mixed feelings at the best of times about these wacky science stories - it's all too easy to make it sound as if public funded scientists are wasting their time on trivia. But if you're going to do it, at least do it in a way that makes sense.
Update - Katy Sheen has kindly pointed out that the i misquoted her - the disappearance was due to Doppler shift, not Lorentz contraction - though the speed was quoted correctly, and so the contract effect would certainly not help with chimneys.