QML graphics fail on one of many machines with "LoadLibrary failed with error 126: The specified module could not be found.".

I am developing an internal tool that uses Qt widgets (some 1500 clients). I wanted to transision to QML+QtQuick. I started with developing one small widget in QtQuick. Now:

• On most machines everything works fine
• On this one machine Qt widgets work fine
• On this one machine QML without graphics work fine (including QtObject, Websockets, XMLHttpRequest etc.)
• On this one machine when I tried displaying a text using Text item inside QQuick Widget i get the error.
• On this one machine when I try displaying a separate QML Window through QQmlEngine i get the same error.

The error is following and it is all the information I get:

I could use some more details: which DLL fails? What more do I need to distribute along with the application?