I don't think this article is referring to physical organisms known as trees (as your article does). It's talking about abstract tree structures, in particular:

1. There is a coherent parent-child relationship

2. Children have only one parent

3. Children have no lateral relationships with other children

4. Relationships are mediated through parents, not e.g. grandparent-child directly.

5. We can coherently differentiate between different children

etc.

All of these are assumptions that greatly simplify analysis and therefore useful in any situations, but almost always fail in some way on closer inspection.

More generally we go to the saying "all models are wrong, some are useful."