I think a 'real store' generally allows you to exchange money for something. If I wanted to sell software to Linux users, Steam is probably the closest thing to an 'app store' you could expect to find. Windows has the Microsoft Store, and Macs have the Apple Store.

Some distros have literal stores. But "Linux" isn't a centralized platform the same way Windows and Mac is. Also, the stores for desktop apps just don't really seem to be as effective. Companies are used to hosting their desktop apps on web.

Games seems to be more of an exception to the rule, for historical reasons.