First, let us define what'a free word order' is and how the word order fuctions in different languages. E.g. Russian or Polish are reputed for being 'languages with free word order', but you never find a preposition at the end of a sentence in those languages.
Within the atlas, Russian is classified as a SVO language (together with Mandarin).
The word order in Russian and Polish carries the meaning of theme/rheme, or the same meaning is conveyed with Japanese -wa/-ga nominative markers.
Speaking on Japanese, its word order is not quite 'free', either (unless we consider phrases like 'watakusi-mo' (me, too) or 'heya-ga!' (the house!) being sentences. Basically, an elaborate Japanese sentence ends up with a predicate. Hence, we need a universal definition for a sentence or, for that matter, for a predicate. Japanese is classified within the same atlas as a SOV language.
In Mandarin Chinese, the word order is used to define what part of speech a given 'word' is. Hence, we should also define 'a word'. According to the atlas, Mandarin falls under the same category as Russian, Finnish or Swedish (SVO).
The two latter languages show a 'free word order', but never in sentences with subject-object clauses (hence, the examples with 'Ali went to school' and 'malchik voshel v komnatu' are wrong examples; the right ones are like 'Ali gave a present to a friend' or 'On arendoval komnatu na paru let').
Thus, the only language on the atlas list with a proper 'free word order' is Hungarian, where the word order conveys the meaning of thematheme/rhemarheme dichotomy.