Execute Dynamic SQL Generated From Select
While I would prefer to generate true dynamic SQL statements with strongly-typed parameters, concatenation is probably ok here because the proper way will be a lot more cumbersome. I do, however, prefer sp_executesql over EXEC(), always.

DECLARE @sql NVARCHAR(MAX) = N'';

SELECT @sql = @sql + N'EXEC [sim].[ROI_Save] ' 
        + CONVERT(varchar(6), VSL.PathId)           + N', '
        + CONVERT(varchar(6), @ROIResultId)         + N', '
        + CONVERT(varchar(6), RT.routeTypeResultId) + N', '
        + CONVERT(varchar(6), RT.ROI_RouteTypeId)   + N'; '
FROM  @routeResultIds AS RT
JOIN sim.ROI_Result_Vehicle AS VSL 
ON RT.ROI_Result_VehicleId = VSL.ROI_Result_VehicleId;

EXEC sys.sp_executesql @sql;


I still don't like that the parameters to the procedure aren't named, and if any of your parameter values were strings or dates, the build-up of single quotes would quickly get very annoying.