I had to search a bit to find the game too. I copied the install link so if you click it, Twitch sings will be downloaded to your PC. You will still need to have a Twitch.com account to play the game. But you don't need Twitch sings to enter the contest, you can make a video using any recording device.
https://sings-download.twitch.tv/installer
Thank you very much lovely lady! :D
I love that little trampoline picture you included, very cool. :D
God bless you. :D Have an awesome day my friend! :D