Very recently, Apple updated its beta iCloud site with support for the Touch Bar on the 2016 MacBook Pro -- but the support is bug-laden, and not fully implemented.
The feature addition, first spotted by MacMagazine, is currently live on Apple's beta portal. The implementation is nearly identical to the one in the macOS Photos app, but doesn't execute as fluidly as the app's does.
Other changes to the online version of the app include a vertical photo album listing, as well as a new toolbar with upload and download buttons.
Apple's Touch Bar, as seen on the new 13- and 15-inch MacBook Pro lines, is essentially a USB 2180x80 display, mounted for optimal viewing at a 45 degree angle. Apple reserves 128 pixels on the left as the "system button," and 608 pixels on the right for the "control strip," including Touch ID prompts -- but not the sensor itself, which sits to the right of the Touch Bar.