Add a gift album already redeemed on my iphone to my iMac

I sent myself a gift album from the iTunes Store on my iPhone. I redeemed it and am able to play it on my phone. I want to be able to play it on my iMac. When it didn't automatically show up in Music (I don't have a subscription), I AirDropped it to myself and it 'sent,' but I can't find it on my computer and it doesn't show up anywhere when I search for it. When I try to download iTunes on my computer, it opens as the Music app. What do I have to do?