**Core Concept**
The hyperkinetic features of Huntington's disease are characterized by involuntary movements, including chorea, which is a type of irregular, unpredictable movement. This symptomatology is primarily attributed to the degeneration of the striatum, a key component of the basal ganglia circuitry.

**Why the Correct Answer is Right**
The striatum is primarily composed of medium spiny neurons (MSNs), which are responsible for the regulation of movement. In Huntington's disease, the loss of MSNs leads to an imbalance in the striatal circuitry, resulting in the hyperkinetic features. The striatum also receives input from the cortex, which is thought to contribute to the development of chorea. The degeneration of the striatum disrupts the normal functioning of the basal ganglia, leading to the characteristic movement disorders associated with Huntington's disease.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the hyperkinetic features of Huntington's disease are not primarily due to the loss of the substantia nigra, which is more closely associated with Parkinson's disease. While both diseases involve basal ganglia pathology, they have distinct underlying mechanisms.

**Option B:** This option is incorrect because the loss of the cerebral cortex is not directly responsible for the hyperkinetic features of Huntington's disease. While cortical degeneration may occur in advanced stages of the disease, it is not the primary cause of chorea.

**Option C:** This option is incorrect because the loss of the red nucleus is not directly related to the hyperkinetic features of Huntington's disease. The red nucleus is involved in the control of voluntary movements, but it is not a primary component of the basal ganglia circuitry.

**Clinical Pearl / High-Yield Fact**
The degeneration of the striatum in Huntington's disease is characterized by a loss of MSNs, which are the primary output neurons of the striatum. This loss of MSNs leads to an imbalance in the striatal circuitry, resulting in the hyperkinetic features of the disease.

**Correct Answer:** C.