It has been argued -- for example by Neo4j, which is one of the leading graph databases -- that index-free adjacency is an essential feature for any real graph database, or as they put it, "Index-free adjacency is the key differentiatior of native graph processing." https://neo4j.com/blog/why-graph-databases-are-the-future/
By my reading, this system doesn't feature index-free adjacency as it uses relational tables as the substrate for edges. Thus EdgeDB won't be especially well suited type of graph traversals and queries that people actually select graph databases for. Which seems like a compelling reason not to identify it as a graph database.
I feel like they make a pretty good case as to why this isn't a graph database, though I wonder if you might expand on your reasoning?