No, the comment by itself wasn't the threat. Explanation here: https://news.ycombinator.com/item?id=49831263 Or just look at this post:

https://www.linkedin.com/posts/jonrichelieu-booth_jonthehash...

It's the combination of the paragraph about the 'delinquent client' and the picture of him pointing a gun which could be construed as an implied threat. I don't know if that would hold up legally, but in any case, no charges were brought in the end.

As to why the police did anything at all, the most likely explanation is that once the 'delinquent client' reported the LinkedIn posts, the Police saw a photo of someone using a shotgun who didn't have a shotgun license. Unaware that the photo was taken outside the UK, they probably decided that the combination of an unlicensed firearm and a possible implied threat was worth investigating.