Screen Output to Projector and Another Computer Recording the Screen
What I have done in the past is to use a DA on the output of the laptop. One output to the projector and another one to the recording device. 

The problem I faced afterwords is that in the chain I had a video switcher and, since we recorded both audio and video, the audio was noticeable ahead. That's a problem if you also have a camera recording the presenter, but not so much if you are only recording the output of the laptop. Later I fixed it in a simple video editor, no big deal, but next time I am using an audio delay in line.