Elementwise dot multiplication for lists of matrices

MapThread[Dot, {{A, B, C}, {X, Y, Z}}]

{a, b, c, x, y, z} = RandomReal[{0, 1}, {6, 2, 2}]

bk = Dot @@@ Transpose@{{a, b, c}, {x, y, z}}
jd = MapThread[Dot, {{a, b, c}, {x, y, z}}]
bk == jd (*True*)

One can also use Inner[Dot, {a, b, c}, {x, y, z}, List] but you need to wrap lists in Unevaluated:

Inner[Dot, Unevaluated@{a, b, c}, Unevaluated@{x, y, z}, List]

See here for explanation.