I think LRU does NOT work with this trick, because there's no easy way to "move-to-front" in O(1) time.
The article mentions Java's LinkedHashMap, which actually can do LRU. But as the name implies, they rely on a linked list, where move=to-front is natural.
But this superpower does not come for free: a Java-style linked hash map will use more memory than the technique described in the article.