I've never had that problem booting games to play straight from my external but I will type the steps to playing them and you can check if you did something wrong. If there is any other information or what the error specifically says Ill try to help.

First off how are you putting them on the external?

A. as GOD files?
B. as extracted ISO's?

I do GOD files because some games can be compressed a bit so you can save memory. But reply with what way you use to put the games on the external(GOD ISO files or anyother way) it would make it easier to help.

How to play games from an external hard drive.

1. Grab yourself an external that is clean and format it to Fat32
2. Make a folder on your newly formatted External HardDrive called "Games" and place your games in said folder
3.Plug your External into your xbox(I was told you get a better connetion through the back port but IDK)
4.If you use FSD then you can go set the game paths so you can then boot off the external from the Xbox Games tab on the dash.

if you downloaded from xex menu then there is files missing but if you put them there via comp then you probly used the iso instead of the gui files