Set triggers and more what I would expect for sights of the period.
That is a model 1874 Sharps in full buffalo rifle dress.
Set up like that they were the Barret .50 cal of the day, not really common. I doubt that a muzzleloader especially one that short would reach out the distance that would require that tall of a vernier sight. Those Sharps had a predictable "rainbow" projectory, and you really had to aim them up in the sky to get them to reach out... and they were packing more punch with a more effective bullet in a longer barrel compared to a short smokepole with a minnie or patched round ball. Notice how much he has that thing tipped up when he is taking aim.
I have a modern .50cal inline muzzleloader with a 24" barrel. It is rated a magnum where I can run 150 grains of blackpowder if I want... but it will only burn a little over 100 before it spits the bullet out the barrel. And I think this shortbarreled muzzleloader would suffer from the same problem if loaded heavy.
I think it is is more of a shorter range target rifle, not intended to reach out 1000 yds like a Sharps... so it doesn't need the big sight.