As you mentioned, test file seems to be 3D images volumes.
There is a Dicom loading massage in dicom Browser as follows.
Could not load: test - as a 2 frames Volume Sequence by ImagePositionPatient+AcquisitionTime as a MultiVolume
Could not load: 1: test as a Scalar Volume
Could not load: test - as a 2 frames MultiVolume by ImagePositionPatient+AcquisitionTime as a MultiVolume
Most data are stored in two large private DICOM tags. One of them seem to be uncompressed, so there is a chance that it can be decoded with some small software development. Are you familiar with Python scripting or can you ask someone at your or at a collaborating institution to help out? We can give advice how to get started.
Are there any export modes/options on your ultrasound system? Maybe if you export the data in a different format then it can be read directly.