I have been looking into this myself, with no conclusive information on how to reliably accomplish this. It feels like Qt 5.6 ought to automagically do the scaling for you; I intend to post a new question in this forum asking about this. In the meanwhile, the first part of this video will be of interest to you:
I am not sure what you are referring to as you app window, but provided that it too is a QWidget you can use QWidget::changeEvent(QEvent* event). In there you can check the event to figure out whether the widget got minimized, maximized or just resized.
From there you can just pass the information to you video player widget and handle it appropriately.
@antemort You can put the 2 gauge images besides eachother inside a RowLayout and add it to the Image element which contains that background image. Advantage of layouts is that it automatically positions the items inside it when it resizes.
As suggested in that link before, em and rem create perfectly scalable sizes. Don't let the name and description fool you: although the size refers to the size of the M character, they can be applied to width, height and any other CSS property as well.