Based on your player's age, the Mizuno Supreme Series: GXC94 Youth Catcher's Mitt could certainly work since if offers a youth fit, but may be a bit heavy at 33.5 inches in size. For your player, I would look at something a bit smaller, such as the Mizuno Prospect Series: GXC112 Youth Catcher's Mitt.
For a 13 year old, you could go after a 34" catcher's mitt if you would like. That length would provide some room for growth. However, since this Mizuno Supreme Series (GXC94 Youth Catcher's Mitt) is considered to be a youth fitting mitt, I might recommend avoiding this mitt.
The Mizuno Supreme Series (GXC94) Youth Catcher's Mitt and the Mizuno Samurai Series (GXC95Y) Youth Catcher's Mitt will have relatively similar pockets. The GXCk94 is a little larger, but I do not believe it is a big difference that you would be able to tell easily.