Oh neat, I didn't know this wasn't a global thing.

It's not as universal as the headline makes it out to be of course, maybe around 0.5% of people host home cafes in smaller towns, it'll be less in the the big cities.

Is it just the old tradition of being hospitable?

Edit: nope. Cafe days is a mix of community celebration and tourist attraction.

Nice article, can recommend reading. For everybody just looking for the answer:

[…] Kodukohvikute Päev, or "home cafe day", when locals turn private gardens, courtyards and garages into temporary eateries for one day in July.

More than 150 such events are held across Estonia between April and September, a beloved tradition that has spread steadily since the first event almost two decades ago. Some are elaborate, with rented tents, tables and chairs; others are little more than a lemonade stand manned by children.

I'd want to visit that garden, place looks picturesque.