Does the Gui/ Ui Designer needs to know how to program?

I am working in the Marketing sector of an Indie game developer, last week for fun I made the game Menu and the HUD in Photoshop and sent to the project manager so that he could use it the game, my knowledge with game creations is very small, so would it be possible for a developer to use my image in the game? For example get an image of a button and make it possible for the button to react when a player clicks on it?

Some places yes, but more often than not, UI designers don't necessarily need to know how to program (perhaps only how to integrate within a set engine, etc.)

When you say, in Photoshop, I'll assume that it is properly layered? (buttons on standalone layers so that they can easily be exported as standalone assets with different states, etc.)

As for button states specifically, you'd either need to make different assets for each state yourself and export them standalone (or on different layers).

Some engines (such as Unity) also allow some cheap out-of-the-box solutions such as using a single button but having a modifier on its colors so that it looks darker when being clicked, etc.