Anyone who wants to can accept the card (technically, the certificate stored on the smart card). For example, I use a domain registrar who registers .ee domains--thus requiring a digital signature from an Estonian ID--and can also use the card as a login mechanism. To be clear, the card isn't an ID in the sense of "here's my ID in person" (the card doesn't have a picture); it is a smart card with two digital certificates stored on it.

More to the point, though, is that Estonia provides a digital identity and signing system that, among other purposes, allows you to access Estonian government services like forming a company. Since you can form a business under Estonian law, you operate as part of the European Union single market.

With an Estonian (electronic) ID card, you can incorporate and run the business online. An Estonian corporation is permitted to do business anywhere in the EU.