To pick the right drug, identify the molecular driver of the tumor and then the inhibitor that hits it.
GIST grows because of an overactive c-KIT (CD117) receptor, a tyrosine kinase sitting on the pacemaker cells of the gut wall. The drug we want must shut down this kinase. Imatinib was designed against BCR-ABL for chronic myeloid leukemia, but it also blocks c-KIT and PDGFR very effectively, which is exactly why it became the cornerstone treatment for GIST.
The other choices target different kinases. Gefitinib and erlotinib both lock onto the epidermal growth factor receptor and earn their place in lung cancer therapy, not in stromal tumors. Sorafenib is a broad multikinase blocker reserved for kidney and liver cancers. None of these matches the c-KIT pathway that defines GIST.
$\therefore$ Imatinib is the agent of choice for GIST.
\[\boxed{\text{Imatinib}}\]