Since it leaps to a creature "of your choice", you don't have to target another creature if you don't want to
The description of the green-flame blade cantrip (SCAG, p. 143; TCoE, p. 107) has somewhat similar wording to that of chaos bolt:
You brandish the weapon used in the spell’s casting and make a melee
attack with it against one creature within 5 feet of you. On a hit,
the target suffers the weapon attack’s normal effects, and you can
cause green fire to leap from the target to a different creature of
your choice that you can see within 5 feet of it. The second
creature takes fire damage equal to your spellcasting ability
modifier.
Before the 2020 errata to the Sword Coast Adventurer's Guide, the relevant line of the spell description read "[...] and green fire leaps to [...]" (which is even more similar to that of chaos bolt); the errata changed that phrase to "[...] and you can cause green fire to leap to [...]" instead.
Rules designer Jeremy Crawford stated the following about green-flame blade in an unofficial tweet from November 2015:
What does the leap effect of green-flame blade do if there are no hostile targets nearby? Does it jump to allies?
The intent is that you can choose no one. If you can't see, you can't choose anyway, and the flame halts
Given the similar wording to the description of chaos bolt (XGtE, p. 151; GGtR, p. 67), it seems safe to assume chaos bolt would work the same way, so if there are no enemies within that range of chaos bolt, you don't need to target someone else.
This is even clearer after the update to the text of green-flame blade (due to the use of "can") - but even otherwise, the specification that it leaps only to a target "of your choice" seems sufficient to indicate that you can choose no target at all. The same logic extends to chaos bolt.
This makes sense to me. Given that if the energy of chaos bolt does leap to another, you choose what creature it leaps to, it makes sense that you can use the same control over targeting to prevent it from jumping to any creature (e.g. by having it fizzle harmlessly against the ground).
The duplicates aren't creatures
Per the mirror image spell description:
Three illusory duplicates of yourself appear in your space. Until the spell ends, the duplicates move with you and mimic your actions, shifting position so it's impossible to track which image is real.
Nothing in the spell description says the duplicates are creatures - they're just illusory copies of you.
...But attacks can always be redirected to them regardless
The description continues (emphasis mine):
Each time a creature targets you with an attack during the spell's duration, roll a d20 to determine whether the attack instead targets one of your duplicates.
If you have three duplicates, you must roll a 6 or higher to change the attack's target to a duplicate. With two duplicates, you must roll an 8 or higher. With one duplicate, you must roll an 11 or higher.
Anytime you're targeted by an attack while mirror image is active on you, the spell can redirect the attack to one of your duplicates. The spell makes no exceptions regarding whether the attack can only target creatures.
As the intro to the PHB/basic rules states:
Specific Beats General
This book contains rules, especially in parts 2 and 3, that govern how the game plays. That said, many racial traits, class features, spells, magic items, monster abilities, and other game elements break the general rules in some way, creating an exception to how the rest of the game works. Remember this: If a specific rule contradicts a general rule, the specific rule wins.
It's because "specific beats general" that any attack that targets you, even if it normally can only target a creature, can be redirected to a duplicate as well.
The duplicates can't be intentionally targeted, either
The illusory duplicates can't be intentionally targeted separately from you. As the first quoted pair of sentences state, it's impossible to track which image is real because they move with you and mimic your actions. Thus, anything that would attempt to target your duplicate would necessarily have to be trying to target you - which of the "duplicates" actually turns out to be you is determined randomly by rolling a d20.
Anything that's not an attack doesn't interact with the duplicates
A later part of the spell description says (emphasis mine):
A duplicate's AC equals 10 + your Dexterity modifier. If an attack hits a duplicate, the duplicate is destroyed. A duplicate can be destroyed only by an attack that hits it. It ignores all other damage and effects. The spell ends when all three duplicates are destroyed.
As the spell itself states, the illusory duplicates have no mechanical interaction with things that aren't attacks - whether it's a spell requiring a saving throw, a non-attack monster ability, a class feature, or something else. Unless it's an attack, it doesn't interact with the spell at all.
(Note: grapples/shoves are "special melee attacks", so they can be redirected to the duplicates - but since they don't have attack rolls, they can't "hit" the duplicate and simply fail if redirected to a duplicate.)
Best Answer
The updated feature in Tasha's Cauldron of Everything is clear.
The feature as presented in TCoE is different:
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.