I can say with 99% certainty, no, you cannot use your laptop's HDMI port as a monitor for the Intel Compute Stick. It normally doesn't work that way (that HDMI is only for Output, not for Input).
Best I think you could do would be TeamViewer, SplashTop, VNC but those all require a network connection (Wi-Fi or USB Ethernet Adapter).
I am not an expert but I would think that that will not work as the HDMI on your laptop would be to send data not receive it.
The HDMI output Port of a laptop is configured in a different way than a input port of a monitor. So I regret to say that this configuration you would like to do is not going to work.