Copper's right about some hardwoods splintering.....it's just the way some woods split, but some would just split, without undue splintering...red oak would splinter where maple would split, not sure about white oak (been several years since I worked with it), though it is a tighter grain & harder that its red counterpart.....if I was making one of those toys, & might opt for using mesquite, hickory, maple, white oak & ash, in rank of hardness...all are tight clean grained hardwoods that would split rather than splinter.....
Your beakasaurus looks like the squares may be 3/8" or even 1/2" stock, while 3/4" material may have been a bit more challenging.....also, I'd think the balls were pretty quickly split open.....
What were the parts strung with?