Baseball IQ Kids is a free browser quiz game covering the parts of baseball kids ask about most: base running, field plays, and the rules that actually come up in a youth game. It runs from Tee Ball through Senior division, so a 6-year-old just starting out and a 15-year-old who has played for years both get questions pitched at their level.
There are five modes — Base Running, Field Plays, Smart Decisions, a Daily Challenge, and Field School, which teaches a rule before testing it. Questions are written from youth league rules rather than pro baseball, because those are the calls parents are standing at the fence trying to remember.
Knowing the rules is the parents' job too. The guides above are free and cover divisions, sizing, and the season.