I was able to get a ripple to appear over the image by using a Stack and wrapping the InkWell in a Material widget.
return new Stack(children: <Widget>[
new Positioned.fill(
bottom: 0.0,
child: new GridTile(
footer: new GridTileBar(
title: new Text(s.displayName),
subtitle: new Text(s.gameName),
backgroundColor: Colors.black45,
trailing: new Icon(
Icons.launch,
color: Colors.white,
),
),
child: new Image.network(s.imageSrc, fit: BoxFit.cover)),
),
new Positioned.fill(
child: new Material(
color: Colors.transparent,
child: new InkWell(
splashColor: Colors.lightGreenAccent,
onTap: () => _launchStream(s.displayName),
))),
]);