There is no regiment, at least no Scottish regiment, associated with that jacket style, as it's purely civilian style, a modern blending of two different military types.
The jackets of the Scots Guards pipers are quite distinctive and cannot be mistaken for anything else, once you've seen one.
Here's a Scots Guards Pipe Major's jacket, with its added silver lace/braid:
Here they are being worn. They've never changed that style, from the mid 19th century till now, except that the front was closed with hooks & eyes, not a zipper. Uinique features include the front style, the scalloped shoulder shells, and the placement of the Pipe Major braid.
The rest of the Scottish regimental pipers wear a doublet like this, green for Highland regiments and blue for Lowland and Guards regiments:
Here's a civilian version of the military doublet. The collar lace and the style of shells marks it as non-military.
Now, what some civilian tailors evidently did was to take the normal Scottish pattern doublet but use the Scots Guards front style, creating the following hybrid:
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