When will you update the theme? The latest version still doesn't work. Another question: In the screenshots there is a thick border around the window. What kind of UI element is it? Couldn't find it in the theme.
Viewing post in Pixel UI Theme for Godot comments
I managed to fix it. It's in the version 1.3 download.
The thick bordered thing is probably a PanelContainer?
Alternatively you can easily override the look for a specific control by overriding in Inspector:
Theme Overrides/Styles/Panel, then add a StyleboxTexture and apply the 8x8_ui_elements.png or a color variation as an AtlasTexture, then select the region you want.