Pick the disease whose growth runs through a tyrosine kinase, because that is exactly where these inhibitors strike.
GIST is the clean fit. Its tumor cells are powered by a constantly switched-on c-KIT tyrosine kinase, and the TKI imatinib turns this signal off, making it the recommended treatment. So this matches the drug class perfectly.
The rest do not. Acute myeloid leukemia is handled with old-fashioned cytotoxic agents like cytarabine plus an anthracycline; it is chronic myeloid leukemia, not the acute form, that responds to imatinib. Neurofibromatosis is an inherited tumor-prone syndrome managed by monitoring and surgery rather than kinase blockers. Small cell lung cancer is a chemotherapy and radiotherapy disease, while the EGFR inhibitors belong to the non-small-cell type.
$\therefore$ Tyrosine kinase inhibitors are used to treat GIST.
\[\boxed{\text{Gastrointestinal stromal tumors (GIST)}}\]