I don't believe there is any existing standard other than GEDCOM, which itself is produced in a variety of dialects. For data interchange, GEDCOM would need to be supported in one or more dialects. It could be extended (into another dialect) to support a wider range of relationships, such as adoptive parents or same sex marriages.
But that's for data interchange. A Wikimedia project could accept and produce interchange data formats while internally maintaining its own model and database; the fact that (some form of) GEDCOM would be available shouldn't have influence on the core of the project.
Personally, I have experience with various software, including phpGedView (earlier form of WebTrees), WeRelate, FamilySearch, WikiTree, and others. I feel a Wikimedia genealogy project would best be implemented on MediaWiki software with extensions for the core entities (e.g. people and relationships). Several existing sites are based on MediaWiki, but the best (but hardly perfect) approach I know of is that used by WeRelate. I don't know the internals of the current WeRelate changes to the MediaWiki software, but I'm sure they would not be easy to simply port over to a modern version of MediaWiki (which would need to be done). However, a reimplemention as a proper extension package seems reasonable.
"What kind of data product does the project envision?" Well, there isn't much of a project at present, just a few people who'd like to see one happen. There's presumably a variety of viewpoints. A "data product" sounds like an export in some interchange format, which is important but somewhat peripheral (What's the data product of Wikipedia, for instance?). Available export/access should include GEDCOM, but perhaps also other interfaces, e.g. something wikidata compatible.
- R. S. Shaw