I don't know if you still have an interest in software that would allow your children to create video games as related here, but I thought I might mention something that might more closely fit the bill.
Clickteam makes a product called "The Games Factory 2". No one is going to make the next 3-D extravaganza on it, but it does a good job in making side-scrolling games and space-shooters of a kind that were popular a few years ago, and with some work one can also make adventure and role-playing games with it. A descendant of the venerable "Klik & Play" franchise, the software starts on a very simple level and allows a user to get more into the works of programming as their interests evolve.
To be clear, I am not being paid to plug TGF2; it's just a program that has allowed me to fulfil some of my own game-design ambitions, and one that sounds like it might be closer to what you hoped for from Games Tychoon. Clickteam's website offers demos of their software if one wishes to give them a shot and see what they're capable of.