How can non-hydrogenated shortening exist?

Most vegetable oils are predominantly some type of unsaturated fatty acid - that is, monounsaturated or polyunsaturated. This type of fatty acid is a liquid at room temperature ("oil"). On the other hand, saturated fat is a solid at room temperature, which is easily demonstrated with butter or animal fat (lard) - which are primarily what vegetable shortening is supposed to substitute for.

Wikipedia has a breakdown of the various types of oils and the proportions of fat types. What's important to note is that while the majority of oils have little to no saturated fat, palm oil in particular is approximately on par with butter, and coconut oil is actually higher than margarine (the most common hydrogenated vegetable oil product).

In fact I've actually never heard of "coconut [oil] shortening" - the idea baffles me because coconut oil is already quite solid at room temperature. It doesn't need to be processed any further to be used as a substitute for butter or vegetable shortening. It's not quite so simple with palm oil though, and there is a "palm shortening" which is different from palm oil.

Hydrogenation is, in a nutshell, converting unsaturated fat to saturated fat by adding hydrogen. Most of the time the hydrogenation is not 100% complete which also leaves trans fats. Palm oil isn't quite as solid as coconut oil so it does need processing in order to be used as a shortening, but hydrogenation is not required; all that needs to be done is to separate the saturated (solid / stearin) fats from the unsaturated (liquid / olein) fats. This is done through crystallization, which is completely different from hydrogenation.

Some companies may indeed also put the coconut or palm oil products through an emulsification process to add volume or make it easier to work with, but that is entirely incidental; these products are made solid due to the very high amount of pre-existing saturated fat and the removal of all or most of the unsaturated fat.

To sum it all up, it's not hydrogenation that makes fat solid at room temperature, it's saturation (of hydrogen atoms), and hydrogenation just happens to be one way to achieve saturation. For products already containing plenty of saturated fat, hydrogenation would be redundant.

An alternative chemical change, called interesterification, is well established as an process for hardening dietary fats. In this case, a direct wikipedia quote seems appropriate:

Interesterified fat is a type of oil where the fatty acids have been moved from one triglyceride molecule to another. This is generally done to modify the melting point, slow rancidification and create an oil more suitable for deep frying or making margarine with good taste and low saturated fat content. It is not the same as partial hydrogenation which produces trans fatty acids.

Apparently at least one company uses nitrogen and whipping to make the oil have a shortening consistency instead of hydrogenation.