Trump's comment made sense to me.

How I viewed is from the a National balance sheet perspective, and given that he has background in Real Estate, it would make sense he too would view the nation in a similar way.

The stock market is part of the NATIONAL ASSETS of the US

As NATIONAL ASSETS increase, the relative size of NATIONAL DEBT is reduced.

1. D/A (Debt/Asset) ratio DECREASES.
2. D/E (Debt/Equity) ratio DECREASES
   
3. Both D/A, D/E are used commonly used leverage ratio's in all business accounting & especially in asset / debt intensive industry of the Real Estate sector
4. Please note: He NEVER said he was going to PAY off the debt with these gains.
5. Please note: he said "maybe in sense". "In a sense" the relative size of debt is decreasing.

TL:DR Here's close, but flawed metaphor. It kinda gives you an idea of where I'm coming from:

wife racks up 10K in credit card debt, husband fixes up the house increasing market value of the house by 5K. You can't really spend the equity. You can't pay your credit card with equity, but your net worth certainly has improved, and the relative size of debt has decreased