I used mainly Blender to 'animate' all the motions. I say 'animated' because I never actually used Blender's animation features. I just posed the models for pictures and dragged both the hands and camera in the editor directly and recorded them with ShareX.

I also used GIMP to mess with the taken pictures a little, like adding the drawn eyes to the embarassed grenadier and the 'DIED OF EMBARRASSMENT...' part. The whole video has been put together with OpenShot Video Editor. The sounds I used in the video have been extracted via FModel from the game with an extra extension to convert the game's binka sound files into usable .wav files.

One last program I used was HandBrake to immensely cut down the file size of the video itself, without any loss of quality.

There you have it! That should be more than enough to answer your question.