When the dictatorship controls the military you can pretty safely say they're a military dictatorship.
But hey, I said what had to be said, and see no point arguing about the formalities. I'll let HN users decide for themselves.
That actually weakens the claim that it's a military dictatorship. If the army is controlled by civilians, its not a military dictatorship. If a person becomes leader of the military due to civilian connections, then it's not a military dictatorship.
A military dictatorship is when a person becomes civilian leader by virtue of their military leadership. If the son of the civilian prime minister first gets to take over the army, it doesn't change the fact that he's fundamentally a civilian and the civilians are controlling - inside and out - the military. It reinforces it. He led the army and the country because of his civilian credentials.
This sounds more like rule by and for a family or a small group of elites.
According to this logic, the United States was a military dictatorship for a good portion of its history. Presidents Washington, Jackson, W. Harrison, Taylor, Pierce, A. Johnson, Grant, Hayes, Garfield, Arthur, B. Harrison, and Eisenhower were all generals. Your claim is absurd.
A military dictatorship installs the dictator and the dictator relies on the support the generals to stay in power.
That isn't the case in Singapore (nor many other dictatorships, where the dictator controls the military).
You can tell by if the dictator has generals replaced, or vice-versa.