OK, sorry for the delay.  The documentation did have a few issues and the internal team is getting those corrections in.

They also sent along this corrected version:

@isTest
private class JobSharingTester {
   
   // Test for the JobSharingRecalc class    
    static testMethod void testApexSharing(){
       // Instantiate the class implementing the Database.Batchable interface.     
        JobSharingRecalc recalc = new JobSharingRecalc();
        
        // Select users for the test.
        List<User> users = [SELECT Id FROM User WHERE IsActive = true LIMIT 2];
        ID User1Id = users[0].Id;
        ID User2Id = users[1].Id;
        
        // Insert some test job records.                 
        List<Job__c> testJobs = new List<Job__c>();
        for (Integer i=0;i<5;i++) {
            Job__c j = new Job__c();
            j.Name = 'Test Job ' + i;
            j.Recruiter__c = User1Id;
            j.Hiring_Manager__c = User2Id;
            testJobs.add(j);
        }
        insert testJobs;
        
        Test.startTest();
        
        // Invoke the Batch class.
        String jobId = Database.executeBatch(recalc);
        
        Test.stopTest();
        
        // Get the Apex job and verify there are no errors.
        AsyncApexJob aaj = [Select JobType, TotalJobItems, JobItemsProcessed, Status, 
                            CompletedDate, CreatedDate, NumberOfErrors 
                            from AsyncApexJob where Id = :jobId];
        System.assertEquals(0, aaj.NumberOfErrors);
         
        // This query returns jobs and related sharing records that were inserted       
        // by the batch job's execute method.     
        List<Job__c> jobs = [SELECT Id, Hiring_Manager__c, Recruiter__c, 
            (SELECT Id, ParentId, UserOrGroupId, AccessLevel, RowCause FROM Shares 
            WHERE (RowCause = :Schema.Job__Share.rowCause.Recruiter__c OR 
            RowCause = :Schema.Job__Share.rowCause.Hiring_Manager__c))
            FROM Job__c];       

        // Validate that Apex managed sharing exists on jobs.      
        for(Job__c job : jobs){
            // Two Apex managed sharing records should exist for each job
            // when using the Private org-wide default. 
            System.assert(job.Shares.size() == 2);
            
            for(Job__Share jobShr : job.Shares){
               // Test the sharing record for hiring manager on job.              
                if(jobShr.RowCause == Schema.Job__Share.RowCause.Hiring_Manager__c){
                    System.assertEquals(jobShr.UserOrGroupId,job.Hiring_Manager__c);
                    System.assertEquals(jobShr.AccessLevel,'Read');
                }
                // Test the sharing record for recruiter on job. 
                else if(jobShr.RowCause == Schema.Job__Share.RowCause.Recruiter__c){
                    System.assertEquals(jobShr.UserOrGroupId,job.Recruiter__c);
                    System.assertEquals(jobShr.AccessLevel,'Edit');
                }
            }
       }       
    }
}

Updated the code with a new example from the documentation team - 12/12/2011

And mentioned that:

"It calls the batch job through the Database.executeBatch() method, which is the recommended way.
 
Note that the customer could make his code work with a quick fix by just declaring the Database.BatchableContext variable and passing it uninitialized to the 3 methods (start, execute, finish) but this is not the recommended way."

Hope that helps.