Why are wave variables a and b normalized to sqrt(Z0) rather than just Z0?
Whenever we do the normalization it is done with some purpose. Here that purpose is simplifying power representation at different points in the two-port network. 
It is clearly mentioned in the 'Power Flow' section of the same document that you posted.


  One of the reasons for normalizing the traveling wave amplitudes by
  \$\sqrt Z_0\$ in the definitions (14.1.4) was precisely this simple way of expressing the incident and reflected powers from a port.


so it eliminates the need for \$ Z_0\$ in power expression. 

Another simple way to look at this is, usually, the power flow in any circuit is represented by terms similar to \$V^{2}/Z\$. Now in order to make power term independent of \$Z\$, you need to divide \$V\$ by \$\sqrt Z\$ and thereafter you will be able to simply analyze the circuit power by considering unit impedance.