Do I actually have to live in Estonia on this permit?

This is a residence permit, not merely a business licence, so it carries a genuine residence obligation. Once your permit is approved you must settle in Estonia and register your address in the Population Register. Being registered as a resident is part of maintaining the permit; failing to establish and keep genuine ties in Estonia can affect both your current permit and any extension. Note that e-Residency is a separate digital ID scheme and does not grant the right to reside.