Why is a comma used to separate hydrogen gas and platinum when using cell notation?
Since $\ce{Pt}$ is not a reactant and only a catalyst, one only wants to write $\ce{H_2}$ on the reactant side. When it is specified, since it is not involved in the reaction, the | is not warranted since Pt doesn't show up in the reaction as the comment by TAR86 pointed out.

Generally, the electrode material is not entered into the shorhand notation since the material of the electrode doesn't change the thermodynamic potential. In this case, the choice of $\ce{Pt}$ is critical and that is why it is specified. The potential of the electrode would be affected by the details of the measurement device with any other electrode material that is a worse catalyst.