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A recent question asked whether it's possible to cause non-magical damage of every damage type, to which the answer was apparently yes. However, a point was raised a couple of times, such as this comment:

It might be worth removing force damage from your list due to its definition. (still a fine question for all other types). PHB. Damage types. Page 196. Force is pure magical energy focused into damaging form

Answers did find a few instances of abilities or features that cause force damage, but which do not match any of the criteria for being "magical" if you go solely by their own description. For example, the ghost's Incorporeal Movement feature:

Incorporeal Movement: The ghost can move through other creatures and Objects as if they were difficult terrain. It takes 5 (1d10) force damage if it ends its turn inside an object.

Going by the list of things which can cause a feature to be considered "magical", this feature is not a magic item, it is not a spell, it does not make a spell attack, it does not use spell slots, and it does not contain any reference to magic in its description; thus this feature is not magical.

However, as mentioned in the comment above, the description for force damage itself does describe it as magical (emphasis mine):

Force is pure magical energy focused into damaging form

Thus my question: Is Force damage always magical damage, even if the feature or ability causing that damage wouldn't qualify as magical otherwise?

Yes, it counts as magical.

You already quote arguably the most specific reference - the definition of the force damage type:

Force is pure magical energy focused into a damaging form.

All force damage is magical. Unless contradicted more specifically in a feature although I doubt this will occur. It is far more likely that they would define an additional damage type or errata the existing definition.

It is also the only damage type that is defined explicitly as magical. One example would be that a dragon's breath is fire damage but not magical; however, the type of damage from the spell fireball is fire and is magical.