The reason why your Liege waffle has breadlike texture is that it is supposed to have a breadlike texture.
While currently in America, waffles tend to have a uniform texture with small variations, and everybody has come to expect waffles within this range, in Europe waffles are any dough or batter baked in a waffle iron. I have waffle books which contain waffles made from batter, cookie-dough-style dough, bread-dough-style dough, and others. They are all baked in a waffle iron, but their final texture ends up being similar to bread, cookies, etc., becasue this is how dough works.
Traditional Liege waffles are a type of waffles made from firm yeast dough, like bread. And the texture is more similar to bread than to a standard American waffle. You didn't do anything wrong, you got the result intended by the recipe author.
If you don't like this type of waffle, you should search for a different recipe.