Unfortunately, the "full" MQA Master experience will not be possible with that model.  The reason being, is in order to fully unfold an MQA file, certain hardware needs to be present.  The NT-503 does not have it since that model preceded the MQA partnership.  Now, you can still listen to partially unfolded MQA files/streams with software (2/3 unfold), but it is not the real-deal.  That is why you can stream MQA via Tidal from the desktop application, but it is not a fully unfolded - all the benefits included - MQA master experience.  

TEAC may update the software to get you the 2/3 unfold, which is still really good, but new hardware would be required to get the last unfold.

No, it's not just you.  I would say that I have heard enough Master vs HiFi file comparisons on Tidal to proclaim there is something to MQA technology.  
The micro detail and dynamic range are the two most noticeable categorical differences for me.  

And you are right, the 2/3 unfolded MQA files (well recorded/mastered ones) still sound pretty damn great!