There are a ton of options.
The easiest one that can be done in any decent video editor, is preparing a transparent shape.
You are used to thinking about the text being the object.
But if you combine it with the big rectangle you now have a rectangle with a hole with the shape of some text.
Put that in a layer above a video and you are done.
For the color, you could make the video with a different blending mode, like multiply, desaturate it and play it above a purple rectangle.
Another option is preparing a mask. This depends on if the program you are using can work with masks. But any decent one will.
You can do that in Premiere, After Effects, or with free software. Davinci Resolve is great and free.
A mask is simply a black and white image.
If your software is simpler and does not accept masks you can use a green text, and cut it using the green-screen option.