Beneath the door is a light switch, hit that then open the door. While the guard is talking walk out the door behind him. It's a small window but doable.
I tried clicking it, I even used the magnifier app, and turned my mouse sensitivity all the way down to click every possible pixel of the light switch, and nothing happened, I don't know what I'm doing wrong? But it isn't doing anything for me.
I tried downloading the phone version, and there I could get it to work via the interact button, but I guess I never considered to press the E key on the PC version, although I haven't tried it yet, all I know is that the phone version works, so try that.