Cycling 74’s “Max” is the perfect product for this, but it’s a bit techie. Lots of tutorials and an active community, however.
The module in Max you want is called Jitter.
There is another module in Max called Gen that will help create Jitter / video widgets.
Also, if you get serious with this, one heads up / suggestion … spend the time getting OSC (Open Sound Control) to work between two computers each running your Max project (essentially, MIDI over a network is kinda what it is, to put it simply). It works over a wired or wireless LAN (just needs an IP address).
That way, you can have a computer or laptop dedicated to just the triggered video clip playback (with a projector attached to it, of course).
Start with just one computer first, of course.
Either way, Max will expose virtual MIDI ports that Cubase will see. That’s how you’ll get the real-time MIDI out of Cubase and into Max.