Yes...for K=10 the closed loop is stable. It is stable down to K=0.5.
In these cases, the gain margin GM is NOT negative (instead, we have GM=+25dB for K=10)
For K<0.5 the closed loop is unstable.
You have made the following error: The function G is NOT identical to the loop gain which is to be evaluated for stability proprties.
The loop gain is LG=-G.
That means: You have forgotten to consider the negative sign at the summing junction where the feedback signal must be subtracted from the input signal (for negative feedback).
The denominator of the closed-loop function is D(s)=(1-LG)