It's not Open Source in the same sense that Unreal Engine is not Open Source. Apparently the term "source-available" license is used to describe software you can access the source but don't have permission do use it freely the same ways as "open source".

Aesprite was open source until 2016 thoughs so maybe the reason it's on the list is the list was created before 2016.

https://www.aseprite.org/faq/#if-aseprite-source-code-is-ava...