Amazingly, Microsoft did not make it easy to tell which version of Windows 8.1 you are running. Logically, you could see "Windows 8.1 Update 1" inside of My Computer, Properties, but alas, they did not do this.
Here are two ways to tell if the update was installed.
Of course, after May 13th, 2014, the issue may be moot: Microsoft is requiring all Windows 8 user to upgrade to this version before this date. Keyliner has updated two machines so far, with no issues; the updates applied without a problem.
Look in the upper right corner of the Tile screen. If you see a power-indicator, you have Windows 8.1 Update 1 installed:
However, after update 2 or 8.2, 8.5, etc., ships, this will not be a reliable way to tell as all new versions are expected to have this same symbol.
Open Windows Control Panel, "Windows Update"
Click "View Update History" on the left-nav
Then painfully look for this KB number: KB2919355
It would be nice to see the version number in the My Computer Properties screen. Perhaps a future patch will fix this.
Other Keyliner Articles of Interest:
Windows 8.1 Slow Computer Shutdown and Restarts
Windows 8.1 CD Drive not Visible in Explorer
Delete Windows.old after upgrade, saving 1G of disk space
Everything you wanted to know about Windows 8.x Tiles