First of al, ATRAC is a strange format. It's optimized for perception as far as I understood it. It doesn't color sound but can reproduce the dynamics and details very well. It's important to understand ATRAC has quality levels: SP, LP2, LP4. SP fits 80 minutes to a 80 minute MD. LP2 fits ~160 minutes, LP4 fits ~320. SP is extremely detailed and transparent. LP2 is really pretty good. LP4 is not good. Is not bad, but for listening on the move. It's not suitable for joy-listening on higher resolution systems. The deficiencies will be definitely heard.
This sound quality has another reason. The DSP/DAC combo on MD players itself. Earlier versions were called Type-R, improved versions are called Type-S. Latter one can reconstruct sound very impressively. It can make SP and LP2 sound really good. It also has a digital amplification section. So, It's only converted to analog at the latest stage. Result is a very dynamic and clean sound. Especially if you convert to ATRAC from CD or any lossless source.
My Hi-Fi (Sony CMT-HX3) also has a 35W version of that DSP/Amplifier combo. It really sounds fantastic* with CD, MP3 and AC3. Didn't try ATRAC, but it won't disappoint I presume.
Sony's higher end systems and DSPs are a work of art. They sound clean, crisp and detailed. They can sing through a pair of good headphones or through 2x85W behemoths. This is why they're timeless and regarded highly. With just Bass & Treble settings, it beats a lot of presumably higher end portable players.
A similar sound quality was present in Creative's Muvo^2. It was plain enjoyable to listen. Apple's iPods famously use Burr Brown DACs but, the sound was too flat and dull in the earlier versions, lacking punch and energy. They fixed it after iPhone 5.
TL;DR: Sony's DSP/DAC/Amp stuff makes any well designed audio codec shine. ATRAC can store dynamics very well. This is why being a Hi-Fi company pays in the portable space.
*: I have a more conventional, but vastly higher powered system. This small guy is not a match for it, but for a small hi-fi it really hits above its league. If you scale this design up (to 80+ watts) with proper speakers, I'm sure that it'll make a lot of more expensive systems sweat.