The 'for' is a way of getting Mr Cawthorn's name to the front of the sentence, to mark him as the topic. It's like 'with regards to' or 'in the case of'. If you take out the 'for', you would have 'Mr Cawthorn youthful brashness' which is not grammatical.
Edit: I hope this answers your question.
Usually, the first part of the sentence would relate better to the rest of the sentence. E.g.
For Mr Cawthorn, youthful brashness is fast becoming a liability.
This sentence is not that well-structured. It starts "For Mr Cawthorn,". This is just to introduce Mr Cawthorn's name. It's a headline, so it needs to say what the topic of the article is. The topic for this article is going to be Mr Cawthorn, and the headline lets us know that immediately. It would be great if the rest of the sentence followed on from that opening a little better, but, sadly, it doesn't.
The writer has a lot of ideas to cram into this headline, and they want to use a dramatic verb like "strike", and they don't have all day to come up with a good sentence. They have basically just shoved everything into a big, long sentence, and the first part ("For... congressman") doesn't flow well with the second part ("youthful ... recklessness"). It's an ugly sentence; I had to read it a few times to understand it. I am not sure if it is actually ungrammatical.