In my reading, what it means by "What’s more, in line with Georgist theory, the tax was supposed to credit owners for improvements they made to the land" is that those improvements are excluded from the tax, IE that the tax is on unimproved value, exactly as you say.

It's true that calculating the unimproved value is difficult. There is no obvious "ground truth" except in rare cases where the improved value has been destroyed and the owner will need to rebuild for some reason. And while there are probably enough such cases to get an estimate of the average in a large city, just taxing against the average would be distortionary (a burden to those with a below average plot, eg distant from metro stations or other amenities) . And to make a more detailed estimate makes the process subject to political maneuvering.