As explained by others, older games with dynamic frame rates will benefit. Of course, future ones will too. What Microsoft is saying is that they can't use it as a performance target during development so all games will be well supported on the old hardware.
I'm not so sure. Rod Fergusson, a developer on Gears of War, made some suggestions of improved performance in Gears of War on the Xbox One S, but I think he was embellishing a bit for the sake of promoting his game. Statements that came out from Microsoft afterwards have said that the Xbox One S has the same performance in games as the Xbox One, and can only benefit from improved color quality with HDR.
http://www.gamespot.com/articles/xbox-one-ss-extra-power-does-not-improve-game-perf/1100-6440933/
Here's a quick copy paste from the above link:
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Microsoft has given GameSpot an official statement, saying the Xbox One S's extra GPU and CPU is not there to improve performance. Instead, it's so developers can make use of the slimmer system's HDR support.
"We have the same SOC architecture as Xbox One today," Microsot said. "For games that want to take advantage of HDR, we gave developers access to a small amount of additional processing power."
HDR stands for high dynamic range. HDR televisions have an expanded color and contrast range, which makes everything brighter and more vibrant. One of the first Xbox One games to support this technology is Gears of War 4, which releases on October 11.
Polygon previously talked to Gears of War 4 head Rod Fergusson, who said the Xbox One S would improve its games' frame rates and resolutions.
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Microsoft has made several other statements saying about as much as well. There's currently no evidence the Xbox One S will be able to run games with higher FPS or resolutions due to a more powerful CPU/GPU.
Although.... if the APU has a die shrink, and the cooling solution is good, there's a chance that thermals can improve, and performance can have a slight benefit from that on some edge cases, but the OG Xbox One's cooling solution was pretty good, so the opposite is just as likely.