I have searched everywhere, but i cant find a way to export my project, so that ue4 will have the media textures included - Is it possible to package the project with the mediatextures included so that it can be opened on other computers?

You simply package the project for your target platform, and be sure your media files are in the /Content/Movies folder.

Medieatexture and packaging projects

anonymous_user_6e7b421a (anonymous_user_6e7b421a) October 27, 2015, 2:49pm 6

Try taking a look at the tutorial I wrote on the Media Player Asset.

Media Player Tutorial

Let me know if you still need help or have further questions.

Thank you,