One of the main functions of present perfect progressive is to talk about a recently finished event that has visible results in the present.
In the case of your examples, this applies because (1) the children are visibly tired, and (2) your eyes are bloodshot and watery.
Let's look at the meaning of the sentences without the continuous aspect:
1-The children are tired now. They have played in the garden.
This means the children played in the garden at some time, not necessarily recently, so there's no connection implied between being having played in the garden and being tired now. Someone might get the connection because of context, but it sounds odd. The nuance that it's recent is lost.
2-Are you ok? You look as if you have cried.
Again, the recent aspect is lost, and "you have cried" suggests "at some point in your life", not necessarily recently enough to have made your eyes bloodshot right now.