They're single-vendor-controlled (and vendor-specific implementation-wise). The question of whether the spec is proprietary is less significant.

SYCL (closely related to oneAPI) isn't single-vendor-controlled. It's a Khronos open standard. If you take a look at the spec, you'll see contributions from various universities, Qualcomm, Huawei, Argonne, Altera, and AMD (Xilinx I think). Intel just adopted it (and bought Codeplay, the original contributor).

oneAPI is a set of SYCL related standards. Originally that was Intel, but now that's owned by the UXL foundation, which is part of the Linux foundation.