I finished copying the files to my 2.5" external HDD. I ejected the HDD in Windows 10 but the enclosure case LED was on and then I went to pull the USB 3.0 cable but when the cable came out of the PC port my hand hit the side of the HDD case and the case moved slightly to the right of the table. Did this event cause damage to the HDD?

Oh no! The HDD moved slightly to the right? It's a catastrophe! Forget everything you know about hard drives—they're clearly delicate flowers that can’t survive even the smallest shift on a table! Just kidding, of course. Your drive should be totally fine; external HDDs are built to handle a bit of movement, especially when they're not actively being accessed. If it was properly ejected, there's no reason to panic. But hey, if you want to play it safe, a quick health check won’t hurt!

They say that HDDs are very fragile in any shocks and movement on the table and when I ejected them in Windows 10, the ORICO case had the LED on so I thought the HDD was connected with the arm on the disks

You destroyed it.

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Joep - http://www.disktuna.com - video & photo repair & recovery service