Cannot use Samples > Data Management > Projections > Batch Define Coordinate System tool with a restricted user profile, as it requires write access to C:\Program Files\ArcGIS install location.
The reported issue, as it is described, cannot be reproduced. Please contact Esri Tech Support if still reproducible.
対処法
Use Data Management Tools > Projections and Transformations > Define Projection in batch mode by right-clicking on the tool Data Management Tools > Projections and Transformations > Define Projection and select Batch.