I haven't heard of this claim before and it certainly sounds suspicious - why would a Christian administration punish anyone for playing with pagan ruins, when it was their goal to belittle paganism?

After searching on google, it looks like most of the websites with this claims are promoting a very anti-Christian agenda (mostly listing Christianity's many crimes). A few has references pointing to a book written by Karlheinz Deschner, who appears to be a very anti-Christian historian writing outside of academic circles. He doesn't seem to be a specialist on Late Antiquity, so I wouldn't particularly trust his words given that I haven't seen any other mention of Theodosius II (408-450) punishing children for playing with pagan statues. (For what it's worth, if anyone has a local German library handy, they can try to find the book Abermals krhte der Hahn, apparently the claim is on page 469)

Having said that, Theodosius I (379-395) was implicated in executing children for destroying statues - Antioch was punished severely when there was a tax riot and rioters destroyed statues of the imperial family (according to Theodoret and John Chrysostom). So it is possible that this claim came about due to a misinterpretation of the sources. After all, both emperors persecuted pagans and Theodosius I did have a particularly turbulent reign (see Massacre of Thessalonica). However, the current academic consensus is that anti-pagan measures weren't particularly harsh in practice (despite continuous legislation) and paganism declined gradually, rather than being persecuted out of existence.