Phosphorylates threonine (By similarity). Not critical for regulating the assembly and disassembly of myosin II filament. ATP + L-threonyl-[myosin heavy-chain] = ADP + H(+) + O-phospho-L-threonyl-[myosin heavy-chain] Belongs to the protein kinase superfamily. Alpha-type protein kinase family. ALPK subfamily.