...arrived and polite man that he is

“Roberto has arrived and polite man that he is, even apologises for being late.”

If I got the construction right, the following could be valid too:
He made a killing overnight and gambler that he was, in no time lost it all. (?)

To me, ‘a’ is required before ‘polite man’ and ‘gambler’.

Use of the article would be wrong.

Eugene, you have the construction right.

It’s not the end of his sentence.