Game with 37 diagonally-oriented holes, 10 black pegs and 10 white pegs
It appears to me that the board you have is a visually stylized version of Two-Player Chinese Checkers. Unlike the regular, 6-player version, the two-player variant utilizes an alternative, smaller board (but can also be played on the regular layout) that could look like this:



While this is the variant I'm familiar with, a quick search also returned this board, which (although presented in a drastically different layout and with a different number of pieces) is used for the same game:



This looks much more familiar to your image, and is equally less diamond-shaped, but still adheres to the basic four-corner principle. Not all variants do, however, like the following one that cuts the sideways corners (which to me seems more true to the 6-player variant):



The last image is identical to your board, with the exception of the outermost rows of three holes.

My guess is that there's a wide variety of two-player Chinese Checkers boards out there, made by people who tried to compress the "original" game down in size to accomodate for the reduced player count. I would put your board in the very same category.