A new computer made in the spirit of the Amiga should have custom chips like Hewitson writes. For a modern computer, this would mean the following:
1. An advanced graphics chip, for example from Nvidia. Obviously with own memory. For optimum gaming performance with LCD screens, it needs to have G Sync.
2. An audio chip with DSP and its own memory for optimum CPU offloading. It might even have several hi-quality hardware sample rate converters for audio processing and recording purposes. That would also enable wavetable playback / hardware synth and audio effects with no CPU loading.
3. Tracked 3D interface, for example something like Oculus Rift as standard.
4. Modern speedy OS. Maybe the hardest task of them all to succeed here.
Many of the hardware requirements could be delivered by a PC or a modern gaming console like the PS4. It 'just' needs a different OS which will allow it to both function as a gaming device (important for the Amiga), but also as a productivity device with (wireless) keyboard, mouse or other interfaces.
Modern games fully written in assembly like the old days is never going to happen. Making efficient code on a modern platform like this is maybe 100x more complex than a classic Amiga, so C++ or similar will have to do (Java go home).