Are multiple Minecraft licenses required to play multi-player?

I bought Minecraft with the goal of playing with my kids, but it appears to be impossible to do this without buying a new license for each kid (that I want to play with concurrently). Am I correct that I am forced to buy Minecraft all over again if I want to play with them?

On PC, you must buy multiple copies in order to play concurrently with others.

However on console (PS3, Xbox) you can both play on the same console at the same time (split screen) with the same copy of the game.

You are correct.

A single copy of Minecraft allows one person to play at once. If multiple people want to play at the same time, each will need their own copy and their own account.