As you indicated in your question, double doun originated from the card game. It can also mean:
To double or significantly increase a risk, investment, or other commitment
When politicians make a comment on someone or something in a seemingly wrong or politically incorrect way, they either back off by making some excuses or double down on (stick to) what they said by restating the reason why they said so.
Trump suggested that George W. Bush bears some responsibility for the 9/11 terror attacks on America and he is being criticized for the remark.
Triple down is a more exaggerated expression than double down as it significantly increasesmore significantly increases the risk of doing so.
The author could have used "double down" in place of "tripple down", but he/she wants to emphasize it is not the first time that Trump doubled down on an issue. Next time Trump implicates someone like Bush in anything, the author might use "quadruple down".