Funny that you mention Memory Alpha, since it expicitly refers to the article at StarTrek.com and it also notices that the planets are so very different that it is highly unlikely they are the same.
Please take a look here:
Oh and since I've recently seen "In the mind's Eye": I cannot remember that there was ever a Kriosian visible in that episode.
At the same time though, MA never insists that there are two different sets of Kriosian races.. again they both have the same type of facial markings.
I think it's most likely a production mistake to be honest. It wouldn't be the first time they've done something like that.
With that being said.. I'm not really sure how this ties in to the request for the Kriosians to be a playable race on the Klingon side.. we don't have to see their planets... additionally we know for certain the Kriosians were a subject species of the Klingons no matter which episode you refer to.
Sometime between the mid-22nd and mid-24th century, the Klingons established a colony on Krios and subjugated the Kriosians under their rule.
In 2367, the Kriosians began fighting for independence from the Klingon Empire. During the revolt, the rebels hid in the Ikalian asteroid belt, where they used the actinides in the asteroids to hide from sensor scans. The rebels later attacked a Ferengi freighter and a Cardassian freighter, in the belt.
For the most part, the Klingons tolerated the rebellion, until Vagh, the Klingon governor of Krios, charged the Federation with supplying the rebels with phaser rifles. Upon further investigation by Starfleet, it was discovered that the suppliers were, in fact, the Romulans, who were planting the evidence in attempt to drive a wedge between the Klingons and the Federation, and to jeopardize the Treaty of Alliance. (TNG: "The Mind's Eye")
The following year, Krios and Valt Minor finally agreed to Ceremony of Reconciliation, to finally bring an end to their centuries long war. The Ceremony was held aboard the Federation starship USS Enterprise-D at a point mid-way between the two systems.