The info on that site is... not even close to correct. Choanozoa as the sister group of all other life including bacteria and archaea? All eukaryotes broken into Opisthokonta, Chloroplastida, and Amoebozoa? Maybe the stuff on metazoans is more accurate, but in the big picture of the genetic diversity of life on earth they're barely a footnote.

The tree only shows species that are selected and their closest common ancestors.

The relationships are obtained from opentreeoflife.org.

Here's an example: two bird species selected via uid share as most recent_common ancestor Passeriformes.

https://sol.vandenoever.info/?uids=695336,1093902

When another bird species is added, one more closest common ancestor pops up:

https://sol.vandenoever.info/?uids=695336,1065606,1093902

https://en.wikipedia.org/wiki/Most_recent_common_ancestor

FWIW, TimeTree is based on phylogenic trees sourced from the the literature:

https://timetree.org

... and publishes references to the literature backing a relationship.

This is important since the tree you get can vary even depending on the gene you study, which can raise some questions about how to interpret these trees.

If you like Subtree of Life, you're going to love 'Onezoom' (https://www.onezoom.org/) which is a very attractive 'Google Maps of life' sort of site, and TimeTree (http://www.timetree.org/) which is similar but the visualisation is much more traditional (not fractals) in comparison with the first.