'玩得转' means you make something is working well as you wish, despite the sophisticated circumstances.
You can imagine the objective perceive as a gear structure to turn around. If the gears get stuck, you can't turn them into the rotary statues as normal, which means it's not working well in the way you like. Such situations can be called '玩不转'. Conversely, the gears are running well can be called '玩得转'.
In the context above, people believed what Trump said which means Trump's words panned out well. Otherwise, if the public didn't convince by his story, it means Trump failed in this matter. The former refers to Trump '玩得转', and the latter means Trump '玩不转'.
Here are some examples:
When the market is monopolized by big companies, will the small companies survive? (or still running well?)
If you want to be a good self-media, a good composition should comes first.
《Big Data 101》, even a novice can pull it off
A man can live well under any circumstance as long as he's solid enough.
Sometimes we just use '玩转', this is more like 'play'. It means to fully appreciate and discover something's many charms
Let me be the tour guide, bring you to discover Beijing's sceneries, snacks, malls, etc.
Play around with English, which means studying English in fun ways, at least not so serious, maybe with an ease mood or interesting content.
Play with cash flow, which means adept at the knowledge of cash flow, including what is it, how to exert it well, and so on.
These kinds of wording often occur in advertisement or promotion copywriting.
It's difficult to have the old learning how to use a cell phone, they can't make it. (Sometimes, 玩不转 ≈ 玩不来 ≈ 用不来 ≈ 不会用 )
His little trick won't succeed in this line of business.
This software is designed for programmers, most people can't master it.
I knew you can't get along all right in political circles.
To sum up, succeed in achieving or winning something difficult means '玩得转', otherwise means '玩不转'
If you get a full understanding on what I'm saying, you‘re really '玩得转' this issue:)