Board Game Arena

Research is under way for my next book about Hive (the first of a series on Hive openings).
Is there a way to access the move by move info for each game played here on BoardGameArena?

Not sure about what you mean exactly. Games can be reviewed move by move from the table result (for example: http://en.boardgamearena.com/#!table?table=8407164, click replay game then choose a player viewpoint). Also on the replay page enabling to choose the player viewpoint you can see the gamelog, but for Hive this doesn't give you the placement info, just the insect being played.

Correct!

But surely, the move information is stored in some type of file (possibly an SGF file?). This is what I am looking for.

Interesting (didn't know about that spec), but we don't rely on a file format such as SGF for replays, nor do we have implemented any system for exporting complete move information for game analysis.

That's too bad.