You’re confusing the use of -include. The -include flag is applied to the path, not the contents of the path. Without the use of the recursive flag, the only path that is in question is the path you specify. This is why the last example you gave works, the path c:\test has a t in the path and hence matches "*t".
You can verify this by trying the following
gci -path "c:\test" -in *e*
This will still produce all of the children in the directory yet it matches none of their names.
The reason that -include is more effective with the recurse parameter is that you end up applying the wildcard against every path in the hierarchy.