The updated feature in Tasha's Cauldron of Everything is clear.
The feature as presented in TCoE is different:
[...] you can use your reaction to invoke the rune and choose a different creature within 30 feet of you [...]
This makes it very clear that the Rune Knight as carrier of the runes chooses the new target.
The feature from UA was not entirely clear
The feature in the UA (which you cite) does not clearly state whether you or the original target choose the new target, neither does it say "randomly chosen", meaning that it should be chosen by someone. Unearthed Arcana are Playtest material which is not checked as thoroughly as the material in source books before publishing.
Looking at the details it seems like you would choose
It is your magic effect which implies that you choose, a priori.
Thematically, the part of the rune that you didn't cite talks about deceptiveness. This implies that other persons present might not even be fully aware of what's happening.
The effect says "you [...] cause that attack to target a different creature”. If you cause the attack to hit someone else, it should be you who chooses. Especially since it can be anyone within range. It is not hitting a random bystander.
Note also, that you hit someone within 30 feet of you, not the attacker or the original target.