So what did they call this jacket?

[MacMillan of Rathdown]

By and large the gentlemen in the photo seem to be wearing variations (shells and trimmings) of what is referred to (at that time) as a standard doublet.

[OC Richard]

Yes, strange as it seems to us today, Highland dancers used to wear long hair sporrans.

Many top pipers in the 19th century made their living by winning cash prizes at Highland Games, both in piping and Highland dancing.

About the name of that sort of jacket, that's what I'm curious about.

An old Henderson catalogue gives:

274. Doublet and Vest, black, navy, or green vicuna, plated buttons, plain lapels 6.

275. do. but silk lapels 7.

276. Celtic Jacket and Vest, black, navy, or green vicuna, plated buttons 5.50

277. Jacket and Vest, homespun or Harris tweed, leather buttons 5.50

This catalogue was issued by one of the leading pipemakers and Highland Dress suppliers at the very time the jacket in the photo was so popular.
So it stands to reason that that style of jacket is either #274 or #276. But which one? Only two jackets are illustrated, one a Day jacket and the other either a Prince Charlie or a Regulation Doublet (the flaps/tashes aren't visible in the illustration).

[HarborSpringsPiper]

The man on the left might have a doublet with standing military collar. . . The board makes me think that this might be a group of Highland Dancers.

I was thinking the man on the far left was wearing a "piper's" doublet too. It appears that both of them on the left are wearing piper's plaids, so less likely that those two are dancers. Also, none seem to be wearing dancing shoes, though I have no idea if Highland dancers at this point were wearing same/similar shoes as today.

You could be correct about them being dancers but when I first looked at the pic you posted on BDBF, I took it for granted they were pipers. Boards were commonly used for piping competitions and it seems even most older pics I have seen of dancers, they were on elevated platforms. Pipers of the period usually seem to have worn the drummer's plaids with these dress doublets, as did the dancers.

Cool pic. Thanks for sharing it.

[OC Richard]

Now in the old days many men were professional pipers AND dancers, earning a good living from the prize money of both competitions.

This isn't dead yet: there's a guy out here who placed in professional piping, Highland dancing, and drumming on the same day at a Games.