I do not understand how this software works.? is it just software that has found a better evaluation that can run on a regular computer with no search?
...i will give it a try...
The evaluation knowledge is stored in an neural network,
and is obtained by selfplay,
instead of classic, handcrafted and tuned evaluation terms.
Deepmind decided to start with zero knowledge in this network,
only the rules of chess were applied,
so AlphaZero it is able to discover unknown coherences
and find moves which are out of human bound.
To train that network Deepmind used 5000+64 TPUs,
to query that network during the match they used 4 TPUs.
How such an design can be ported to common hardware is matter of discussion.
So, yes, in the optimal case, AlphaZero would perform only a depth 1 search and already find the best move.
But in front of the neural network they perform an selective Monte Carlo Tree Search
with 80 Knps (single node, 4 TPUs).