There are some trends. Types to the right are "subsets" of types to the left; e.g. a &mut T can coerce to a &T, similarly, you can box a T into a ~T, or take references to get an &mut T or &T.
periodicity refers to (originally) that the trends are cyclical with respect to atomic mass - we now know that it's with respect to atomic number and that the period increases (2 - 8 - 18 - much more) but nonetheless between multiple rows there's an increasing valence. Hence there is a repeating aspect 'period' driven by a connection between row n and n+1 (row n+1 immediately follows row n in atomic number). There's no connection between row n and row n+1 in this table of rust types. The vertical organization is completely arbitrary, there is no ascending value across the table, and therefore it's not periodic.