I‘ve NEVER seen any headphone amp in the world using “bridged” for balanced ‘phones out.
If RME started with it, people wouldn’t understand.
Technically the term balanced is correct, same “weight” with opposing directions on both branches of the signal wire.
It’s EXACTLY the same schematic like an active “balanced” line out, which no one would call “bridged” - a less correct term BTW - where is that “bridge”?
Balanced phones amps technically use “differential” signal out, like most of the line out variants below.
This is again no reason to use that label here.
Next - it’s not RME’s fault - and nobody else’s - that for signal transfer multiple variants of balanced outs are possible:
• Transformer balanced without ground reference.
• Transformer balanced with ground reference.
• Active electronically balanced with level compensation when connected to single ended destination.
• Active electronically balanced without level compensation when connected to single ended destination.
• Impedance balanced.
All the above without, and with source/destination impedance matching (for long distance and/or high frequency interconnects).
It’s a plus that RME mentions the used variants in the manual, even giving connection advice.
This information is important for proper use, in a complex recording studio environment e.g. it can make a difference.
Finally - in all cases the balanced noise suppression happens in the destination only BTW, by no means in the source.