[RPG] Can Force effects from the Border Ethereal affect targets on the Prime Material

No, force damage does not affect creatures on the Ethereal Plane.

As quoted in the question, the DMG states that:

solid objects on the overlapped plane don't hamper the movement of a creature in the Border Ethereal. The exceptions are certain magical effects (including anything made of magical force) and living beings.

This specifically relates to movement. Force damage is not the same thing as a "thing made of magical force." This is confirmed in an unofficial tweet by Jeremy Crawford addressing this specific question:

Q: Do Magic Missile and Eldritch blast, which do force dmg., affect creatures on the ethereal plane, if they can be perceived?

A: No general rule causes force damage to pass from one plane of existence to another.

So even if you can perceive a creature on the ethereal plane, you cannot damage them with force damage.

Here is a later tweet response which states the case even more explicitly:

Q: Then what is the intent of DMG p. 48 "including anything made of magical force"? If no damage, would EB push cross planes?

A: Ethereal Plane: the DMG refers to things, like wall of force, made of force, not to the force damage type

I think it's indeed only in respect to hampering movement: "certain magical effects (including anything made of magical force) and living beings hamper the movement of a creature in the Border Ethereal".

I'd interpret this as follows:

• Forcecage and the like are impassable.
• An ethereal creature abides by (only) the following parts of the "Moving Around Other Creatures" rule on page 191 of the Player's Handbook:

Whether a creature is a friend or an enemy, you can't willingly end your move in its space.

lf you leave a hostile creature's reach during your move, you provoke an opportunity attack [...]

I wouldn't consider a material creature's space difficult terrain for an ethereal creature to pass through. Ethereal and material creatures still can't touch, grapple, or physically attack one another except via force effects, so those opportunity attacks are going to be hard to exploit.

I suspect the RAI is solely to keep ethereal creatures playable on a grid. It'd be a real headache if they were constantly overlapping other creatures' squares, even if it's what ethereality logically enables.