Desktop PC's can Hibernate or go into Standby or be fully shut down.
The ACPI (Advanced Configuration & Power Interface) standard provides a standard for linking hardware, including the processor to the BIOS and to the Operating System. The ACPI standard ensures that hardware, BIOS and OS from different manufacturers have a common power management system. All standard PC BIOS chips conform to the ACPI standard.
Even if a PC is 'shut down', some components may still be powered, usually depending on settings in BIOS. The wake on LAN function is well known and allows a 'shut down' PC to be switched on by sending a particular message to the Network Interface Card.
In your case there is obviously a wake on Mouse enabled.
Other options include wake on Keyboard, wake on Time and wake on Modem. Implementation varies from motherboard to motherboard.
I would start in the BIOS and look at power settings.