The structure I need for my particular project (ConceptNet) is:
* The definitions from each Wiktionary entry.
* The links between those definitions, whether they are explicit templated links in a Translation or Etymology section, or vaguer links such as words in double-brackets in the definition. (These links carry a lot of information, and they're why I started my own parser instead of using DBnary.)
* The relations being conveyed by those links. (Synonyms? Hypernyms? Part of the definition of the word?)
* The links should clarify the language of the word they are linking to. (This takes some heuristics and some guessing so far, because Wiktionary pages define every word in any language that uses the same string of letters, and often the link target doesn't specify the language.)
* The languages involved should be identified by BCP 47 language codes, not by their names, because names are ambiguous. (Every Wiktionary but the English one is good at this.)
There are probably analogous relations to be extracted from Wikipedia, but it seems like an even bigger task whose fruit is higher-hanging.
Don't get me wrong: Wiktionary is an amazing, world-changing source of multilingual knowledge. Wiktionary plus Games With A Purpose are most of the reason why ConceptNet works so well and is mopping the floor with word2vec. And that's why I'm so desperate to get at what the knowledge is.