When a computer sends a frame to another computer do other computers on that network receive the frame?

That would depend on the network topology chosen and the type of network connectivity devices employed.

In a properly constructed, switched and/or routed network the answer would be NO.

If hubs or repeaters are used to connect devices and/or network segments, then yes.

In a bus or ring topology, the answer is yes. Whether anything is done with the frame is a different matter and depends on whether you consider the network adaptor to be integral to the computer.