You could create an app with App Designer. See video below:
You could display the video on a uiimage or uiaxes. For the button you can use a uibutton. All of these uicomponents can be dragged onto the canvas (uifigure) within App Designer, which will automatically generate code for you. You can right click the uicomponents to add callback functions (in your case for the uibutton to log when the user clicks the button. You could utilize the built-in functions tic and toc to record the time in which the button was pressed.
