I am not the super-techie that many of our fellow members are, but I have not bought a desktop since the 1990s. I have been building them. It is like going to your local auto parts store, and finding that the really hot really feminine gal on the other side of the counter can teach you a few things about your car, its engine and how to fix it. Now to be straight (no pun intended) I am a guy, and there is such a woman at my local Advance Auto. I digress.
What you may be seeing is the result of the projector's demand on the entire system. I would guess that your CPU, RAM and hard drive virtual memory space and speed have to be factors. Further, your video adapter solution could also be a culprit. Oh, and don't forget your motherboard. Are you using AMD or Intel? What is your clock speed and core count? Are you using onboard or external video adapter? How much RAM and how fast are the RAM sticks? Is this ethernet or wireless? Is the projector a local or network connected device? What programs are running in the background? Is there any malware present? What color socks are you wearing? Oops! That's what I say when I call the gal at the auto parts store.
What I am thinking is that your machine is prioritizing local over network, i.e., running local devices and programs first then somewhere down the line budgeting for external processes and devices.
Again, this is only the guess of a sophomoric somewhat advanced pseudo-super user.