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The 64-bit VST2 version opens fine but seems only partially functional to me. I can load a previously made in BIAB SGU, but it doesn't play within the plugin when Play is clicked. It will, however, successfully transfer the tracks to Mixcraft.

You need to generate up the tracks first.
It will then play back in sync if you have other tracks in Mixcraft or you can File > Preferences > uncheck Sync playback, now select the track in the plugin and hit the plugin Play or double click the chord sheet bar to play from there. you can unfold it with the down arrow in the bottom right.
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Additionally, when I try to sound out a chord in the plugin with BIAB's Shift+Enter command, nothing happens, except that the chord in the selected cells is erased.

That's one of the million and one features of Biab application,
the Plugin is more for DAW only users that don't want to go through the steep learning curve of Biab and just want create tracks directly in the DAW, maybe to add to an existing session.
Like if you have a recorded session and want to add some extra tracks or solos in certain section you can use the MultiRiff function soloing each track in the plugin while playing back in sync to choose what track fits best to your recorded tracks then drag that track in to the DAW.

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Am I misunderstanding that BIAB's DAW plugin can be used for composition and arrangement within a DAW? Or, is the idea to do this in BIAB directly, then open the saved SGU in the plugin, to transfer the parts to tracks? If the latter is the intent, then , the older method of drag and dropping into a DAW seems more practical.

Yes if it has a lot of complexities stick with the Biab application and just drag the tracks out into the DAW.
Biab Plugin & ReWire