A username lookup field renders as a picklist on Inventory Orders for profiles with Modify All object permissions.
The user field for Administrators is a standard user-lookup field on the Inventory Order page layout. All other users have a picklist field. Administrators are identified based on the Modify All setting at the profile level.
This is working as designed.
Modify all data permissions should be set on the profile level on objects as well as under the Administrative Permissions area of the profile. This setting is only available for users with System Administrator profiles utilizing a Salesforce license.
CRM Help Documentation: Sample Inventory Order Configuration