Is finding Kth largest element using selection algorithm taking O(n) only if K is fixed?
There is no requirement that $k$ be constant, and those StackOverflow comments are misleading or simply incorrect.

Obviously $k \le n$ and so $k$ is $O(n)$. Your partial bubblesort algorithm is $O(kn)$ which is $O(n^2)$ unless $k$ is somehow restricted.

But the Quickselect algorithm is stochastic $O(n)$ and can be made worst-case $O(n)$ by using the median-of-medians algorithm to select the pivot. (Median-of-medians is too slow for practical use, but it proves that $O(n)$ is possible.) Quickselect does not require $k$ to be fixed.