Cherry tree: i think it has rotten roots (pics)

I can't see anything obviously wrong with the roots.

But.....

1.
The roots look like they're rather matted/tangled and in danger of strangling each other unless you untangle them (you'll break some roots when untangling, but it'll be fine).
If the tree lives in a pot, then some degree of tangling is inevitable.
But tangled roots will not grow outwards as readily - if you plan to plant it in the ground, it will be slow to establish. If it is to be grown in the open ground, I suggest "clawing" with your fingers at the outermost inch of the compost, to knock the soil off and allow some roots to dangle freely.
When planting, dig a hole larger than the rootball and spread some of those "dangling" roots into the surrounding soil, so help increase the root spread without the tree having to grow new roots.

2.
The rootball looks very wet and although the roots may be that wet just after watering without suffering long-term problems, if they remain that wet for more than several hours at a time they will literally die from drowning (oxygen deprivation) .

I was thinking the roots look rather waterlogged.

Ian