That "Template" line... this one...
... is a required field for child themes. That is what tells WordPress that this is a child and not a stand-alone theme, and also which theme to use as a parent. Files not replaced by the child theme are loaded from the parent.
Without that "Template" line you are bound to have problems but how many problems you have depends (I am speculating) on how much the child depends on the parent. If the child replaces only one or two parent files you may have a lot of trouble. If the child replaces nearly everything, you may not notice the problem. And of course a lot depends on which files are replaced and which should load from the parent.