You can use ffmpeg to do something like this programmatically. It has the capability to composite and edit footage as well as adding effects and text. It is a command line app, so works in the shell of your choice on Linux/Mac/Windows. Youtube reputedly uses ffmpeg to process their videos, so it's safe to say that it's very widely adopted. FFMPEG is free and open source. This is probably your best bet.
Adobe After Effects can also be controlled completely programmatically using the Extendscript language. After Effects is an industry standard video effects tool, used for everything from web banners to Hollywood movies. While it has more capabilities than ffmpeg, it is mainly designed as a GUI application, and the API really needs a good understanding of the application to use, meaning that developers are probably fairly hard to find. It is available from Adobe through Creative Cloud membership.
Coding the solution is another option. Rather than re-invent the wheel you could look at one of the frameworks that exist for creative coding. One of the most popular is Processing; it's a programming language designed for creative use, based on Java. Although not specifically focussed on video it does have the capability to process video, and could add text and effects to video content. Similar tools exist for other languages, for example OpenFrameworks, which uses C++, and Nannou, a relative newcomer which uses rust. To use them you will need programming skills, but a lot of the heavy lifting has been done in terms of things like graphics and video, meaning you can work at a higher level.