To the best of my knowledge, Windows only supports client mode, ad-hoc mode, and AP mode for network controllers. Hybrid modes for a single NIC isn't supported, only bridging between two NICs (so one in client mode to the router AP, and one in either ad-hoc or AP mode to other clients).
I know Linux allows greater control over the networking stack, but I've never heard it allowing hybrid modes. But I don't know enough Linux to comment.
I'm curious why the other clients can't just access the same AP your laptop uses. I would guess university or hotel WiFi, which might have stricter access requirements, but there are tools/dongles designed to help with those exact cases.