I played Black Mirror in the right order but there was such a long gap until the 2nd & the 3rd (both of which I thought were great!) so I'm not sure the order mattered there except for playing 3 after 2!
I played Gabriel Kinght 3 first, then 2, then 1 in the order of accessibility (a few years inbetween!) I didn't think it mattered too much as the stories are complete in themselves but I did learn better about the background of Gabriel & the relationship between him & Grace when I eventually got to play the earlier games!
The only other series that I can think of playing out of order was Discworld - I played DW Noir 1st followed by DW2 & then a few years later I eventually got my hands on DW 1 - I don't think the order mattered at all - they all seem to be self -contained & I love them all!