I've looked at and enlarged the better image found by kootne and there does seem to be something on Touch the Cloud's belt or more likely his right braid that together with the rifle being angled is the source of the action's "strangeness".  In any case, it's certainly a rolling block.

Bill Lawrence

Here is another of GAC with his rolling block rifle and a nice bull elk. I know for years there has been speculation about those rifles being the same rifle but I personally think the barrel is shorter in the Custer/elk photo than the one Touch the Cloud is holding. Remember George was about 9" shorter than the Indian. But both rifles do appear to round tops with heavy barrels.

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Well, I dug out a heavy barrel sporter (30.375" barrel) for comparison measurements. The GAC/elk picture doesn't give a good view of the end of the forearm so I compared length of receiver to barrel length. I am putting it at ~28.44"
On the Touches the Cloud rifle I measured the forearm and barrel and using the forearm length of my rifle (10.875) I am putting his barrel at ~30.5"
I blew the pictures up and used a Mitutoyo dial caliper to measure the pictures and a tape measure to get the rifle measurements.
I don't think they are the same rifle. 
ymmv
I do think somewhere I heard the serial number of GAC's sporter was 3535 but that seems late for what looks like a roundtop. I only remember that because I have one #3735

Dennis
p.s. to the OP, I love the comment added to the picture!