Hello gmatt25!

Problem is you haven't made it clear whether the code inside keyPressed() is successful at changing which video is playing.

I have a command coming in from OSCulator which defines that, but then I feel I need to start using booleans etc.

Command coming and define that...?
You need to determine by yourself which role the pieces of your program are responsible for.
Whether OscP5 or keyPressed() is tasked for changing the current playing video!

Oh sorry! Now I've got it!
It's just I don't have a Wii control nor any of your videos to play!

Just a wild guess -> I don't think keyPressed() or mouseClick() can detect a Wii control.
Have you looked for some instructions on how to use OscP5 library already?

Here's some post related to this library:
problem-receiving-arguments-from-an-osc-message-oscp5-osculator

I don't have much idea how all that works.
Just took a peek @ oscP5plug.pde example.

I guess what you need is a "current button state" type variable, since a boolean can only store 2 states.

byte videoButton;

I guess this may work, that is, if your Wii joypad really sends a float data-type variable!

final static byte Left  = 1;
final static byte Right = 2;
final static byte Up    = 3;

byte videoButton;

void buttonLeft (float press) {
    if (press != 0 && videoButton != Left) {
        player = new GSMovie(this, "tdogg.mov");
        videoButton = Left;
    }
}

void buttonRight (float press) {
    if (press != 0 && videoButton != Right) {
        player = new GSMovie(this, "bunny.mov");
        videoButton = Right;
    }
}

void buttonUp (float press) {
    if (press != 0 && videoButton != Up) {
        player = new GSMovie(this, "transit.mov");
        videoButton = Up;
    }
}

Well, seems like we need another boolean variable -> playCamOrVideo .
When it is true, play a webcam feed, otherwise play a video file.

I've never used any external library for Processing.
So I dunno which method makes a video/webcam to start/stop.  

So I'll just assume player.stop(); & cam.stop(); makes them stop!
Just fix that if I'm wrong, OK? 

Just an observation -> final static byte number2  and such are not arrays, but normal variables w/ immutable values!
It's just a sugar name to represent an idea.

So, instead of saying -> if (videoButton != 3) , which is cryptic.
I just ask -> if (videoButton != Up ) , which is much clearer its intention!

So just like your example I have set a new void for button 2...

Void just means that a function/method returns no value!
It's much clearer to say I've made a new function or method for button 2...

Last observation -> Are you related to rickyc123 from thread webcam-in-array ? 

final static byte Left  = 1;
final static byte Right = 2;
final static byte Up    = 3;
final static byte Btn2  = 5;

byte videoButton;

boolean playCamOrVideo;

void draw() {
    image(playCamOrVideo? cam : player, 0, 0, width, height);
}

void setDevice(boolean webcamOrVideo) {
    if (webcamOrVideo != playCamOrVideo) {
        playCamOrVideo = webcamOrVideo;

        if (playCamOrVideo) {
            player.stop();
            cam.start();
        }
        else {
            cam.stop();
            player.loop();
        }
    }
}

void buttonLeft (float press) {
    if (press != 0 && videoButton != Left) {
        player = new GSMovie(this, "tdogg.mov");
        videoButton = Left;
        setDevice(false);
    }
}

void buttonRight (float press) {
    if (press != 0 && videoButton != Right) {
        player = new GSMovie(this, "bunny.mov");
        videoButton = Right;
        setDevice(false);
    }
}

void buttonUp (float press) {
    if (press != 0 && videoButton != Up) {
        player = new GSMovie(this, "transit.mov");
        videoButton = Up;
        setDevice(false);
    }
}

void button2 (float press) {
    if (press != 0 && videoButton != Btn2) {
        cam = new Capture(this, cameras[0]);
        videoButton = Btn2;
        setDevice(true);
    }
}

1. //This block of code would still appear in setup to bring in the starting video..
2. GSvideo setup
   player = new GSMovie(this, "tdogg.mov");
   player.loop();

I'm also learning Processing/Java. I just thought that teaching what I know and searching what I don't would make the process easier!

Just be aware the code above is just suggestions that you have to adapt for your own full program.
Most of the variables are not declared for example! Just what I've invented!

Another thing is that I can't run your code. So I'm blindly trying to help you out.
Only you 2 can test whether it's working!

And as I've mentioned, I have no idea what methods make a video/webcam to start/pause/show-up/stop in those libraries!

Within setup(), if you want a default video to start playing, make sure to also set flag variable videoButton corresponding to it.
For "tdogg.mov", that would be videoButton = Left.
This way, if the user presses Left button, the video doesn't restart, since it's already selected & playing!

For what I've understood you, you want either a video or a webcam showing up.
So, if Bnt2 is pressed, any video playing should stop and webcam would replace it.
Of course, if webcam is already active, no need to waste time stopping the video and restarting the cam.

The opposite is true for Left, Right & Up buttons, stop webcam feed and start corresponding video if it's not already active!
That's why I've created function setDevice(boolean).
If true is passed to it, it tries to turn off the video and turn on the webcam. Otherwise, the opposite!

Within draw(), we have function image() to draw an object to the canvas screen.
I believe cam is a frame image from webcam, and player for a video file, right?

playCamOrVideo stores the state condition if it's a cam or a video which is active.
If it's true, the webcam is active, otherwise one of the videos is.

playCamOrVideo? cam : player is a compact if/ else condition.
? : is called ternary operator type, because it demands 3 operands to function.
If playCamOrVideo is true, use the reference value stored in cam, otherwise, use of player's!

That's all for now. Any doubts, just ask! Good luck!!!

When you declare/create a variable inside a function/method (or even inside a loop block, etc.), that variable exists only inside that domain/scope.

Let's say you created variable cameras inside function setup().
Then, only setup() knows and can access that variable!
It's a local variable bound to setup()'s scope!

As I kept warning you, my code is very incomplete.
You have to adapt and merge it back to your main code.

Your program depends on the existence of variables player & cam, cameras[], etc. being accessed by all functions everywhere.

That's why they need to be declared outside of any function, of any curly brackets!
So they can become global field variables of the sketch itself.

The other more "professional" option, is passing them as function parameters.
This way, a function communicates to another its own local variables!