Liberalism and democracy are two different things. Liberals believe in both, but just because you are a Democrat doesn't mean you are a Liberal as we see in the Democratic Party. Or if you are a small d democrat, meaning you are someone who believes in democracy, but you are not a member of the Democratic Party like let's say center-right Republicans. So you can be both someone who believes in liberalism and democracy, but you can believe in another lets say democratic oriented ideology that believes in at least certain amount of individual freedom and believe in democracy as well.
Now there is also liberal democracy which is what the two men in this video were talking about to a certain extent. Liberal democracy would be a national system or governmental system where we have democracy based on lets say liberal values. Where everyone is treated the same and fairly under law. Where we all have a certain amount of individual rights and liberty under a Constitution that can't be taken away even if there's some democratic or majoritarian will to do so. Which is how the American founding fathers set up America. A liberal democracy based on liberal values and constitutionalism.