Though it is described as pretty remote here (along a road north of Merke)
If I can make correct sense of the Dutch the page is referring to a Sanitorium at Oytal - a "suburb" to the NE of Merke.
I think the "real" Merke Sanitorium is in the mountains/valley to the south of the town.
See - http://www.smerke.kz/
But the hotel's Web site makes absolutely NO mention of any cultural sites nearby!! People obviously only go there for the Sanitorium aspects! (Though it does figure on the itinerary of a number of botanical tours visiting the local flowers)
You will see the anthropomorphic "Bal Bal" stones at Burana tower by the way!
This report (free download if you register) titled "GUIDE TO KAZAKHSTAN - SITES OF FAITH - SITES OF HISTORY
" (Actually this is a comprehensive guide in book form of historic sites across K) has a complete section on Merke (6.12) plus sections on very many other historic sites. I quote what it says about the location of the Sanctuary - "Amongst the mountains of the Kyrgyz Alatau, approximately thirty eight kilometers south-southeast of the town of Merke, on an upland traversed by the river of the same name and its tributaries, stands a vast area sacred to the ancient Turks, which over thousands of years has been enriched with numerous commemorative complexes that differ in type and period."
See - https://www.academia.edu/1117252/Kazakhstan._Sites_of_Faith_Sites_of_History?auto=dow nload