100% direct democracy can mean different things based on your definition of the term. The concept of limited direct democracy is not brought up in this idea construct you have. In a limited direct democracy, there is no mob rule because the outcome is limited to constitutional boundaries to prevent rights of others from being violated. When no rights are violated, it's lawful and it's not mob rule as in "unlawful" rule.
Direct democracy is a value, not a form of government. It can be lawful, it can be used to repeal government tyranny of the minority as well.
All ducks are birds but not all birds are ducks. It's important to understand this when dismissing direct democracy as a tool to be used for the ending of tyranny instead.
The moment you decide to vote up or down here on Steemit, you're using direct democracy not based on facts, only opinion. In a modern direct democracy, that distinction would be further advanced than what Steemit has enabled. If you don't like voting, you wouldn't be on Steemit in the first place, it's a voting platform using money, like a government with differnt rules.
Even steemit has no filter for useless opinions that are simply popular.
Your debate point used no facts other than wikipedia which everyone knows is limited, and Orwell's film, a fiction. The very definition they give, that direct democracy is a pure democracy is false. Both are different.
A pure democracy is a form of direct democracy, but a direct democracy can also be a limited direct democracy.
I write about this subject so feel free to follow to engage in any debate you may have about the topic. Only direct democracy has the power to give people the right to supecede our governments limitations on us and choose to remove or create policy we need without relying on them. It's not statist, reliant on them, it's within lawful paramaters, not violating the NAP as long as the policy created or removed doesn't, and it's practical in the real world with application time in two years rather than a lifetime of just wishing for a better world to happen by the free market already.
When given the abillity to vote, say for a removing government power over others taxes, that does not cause harm and voting is not violence, it can end violence and there are many cases of referendum and initiative used in accordance with more libertarian ideals.