File "type" is just a simplification. On modern operating systems all disk files are equal from an OS point of view (they're just sequences of bytes) and the "type" of a file only depends on the program that read/write those files. In the past a lot of operating systems used to discriminate e.g. between binary files and text files but those times are almost completely gone.
A common approach to make the type of a file "evident" is to use a naming convention... i.e. a file with a name ending in ".mpg" is probably a video file encoded using MPEG standard, or a ".txt" file probably contains human-readable text.
Therefore you have two options... either you just filter the file list depending on the file names (e.g. you only accept files ending with ".mp4", ".mpg", ".mpeg", ".avi", ".wmv", ".webm", ".ogg" ... - just to name a few common video files extensions) or you just try to pass any file to the program and the program will decide if it can play it or not. If the program is a good one it will fail gracefully if it can't understand a specific file format instead of just crashing.
Note that even if you're using Qt (a portable library) I'd wouldn't be surprised if what are the accepted video file encodings depends on the operating system and even on the single installation (because video/codecs codecs are often "plugins" that may be or may be not installed on a system).
If you really want to limit the file names then please remember to add a way to select a file with an extension that it's not in your list. Every single time you enumerate things in your program you are first of all sort of arrogant (a list implies that you know all possible cases, do you think you really do?) and you are placing an obstacle to future compatibility (e.g. next version of the player program will handle also .wzz video files but your program will not able to play them because of a stupid limitation in the list of allowed extensions).