Playing background sounds while talking in Skype

The easiest way to do this is to have your background sounds on your Skype audio is do do this via hardware; have the audio on a different set of speakers the microphone (or input device) can pickup.

It can be Bluetooth or USB (easier). You can't use the headphone port because when you plug in the headphones, by design, the internal speakers of your Mac will disconnect. For example, I use the Behringer UCA202 USB Audio Interface to connect my Mac to my audio system. All music and audio from videos etc. are piped to this device. System sounds are relegated to my internal speakers.

Skype audio (mic and headphone) are through the internal devices. Additionally, I can mute my calls/music/whatever from this device without muting my system sounds; just by hitting mute on my audio device's remote.

However, when I play music or videos, I pipe the audio through the USB

So, if you need your Mac's background noises to be heard, you can pipe your System Sounds through the USB audio leaving Skype with the internal audio devices; or vice versa. They will hear it.