By "buying the song" on Gumroad you don't actually buy the song, you buy the right to do specific things with that song. I couldn't find the exact license terms, but for 800 Yen (about $6) for a whole album I highly doubt that this will include much more than the right to listen to the song on a private device.
The rights to publicly perform, reproduce, redistribute, use commercially etc. usually cost a lot more.
So if you want the rights to use the song in your own video, you will have to negotiate the purchase of a license which allows you to do that with the creator. Or if they reassigned their copyrights to a music label or copyright collective (which some music artists do), with that organization.
There are some exceptions in the copyright laws of some countries where you can use parts of a song without a license. For example, the "fair use" exception in US copyright law if you review, discuss or analyze a song. But such exceptions usually don't apply if you use the song as background music, adapt the song into an own work or even just reupload the song on your own channel.