I have a batch apex job and the code is as follows

global Database.QueryLocator start(Database.BatchableContext BC)
	{
		return Database.getQueryLocator(query);
	}
	
	global void execute(Database.BatchableContext BC , List<sobject> scope)
	{
		List<Test_Key_Event__c> keyEventsToInsert = new List<Test_Key_Event__c>();
		
		List<RecordType> recordTypes = [Select r.Id, r.Name, r.SobjectType from RecordType r Where r.SobjectType = 'Test_Key_Event__c' ];
		
		For(sobject s : scope)
		{
			Contact con = (Contact)s;
			
			For(ActivityHistory task : [Select c.AccountId, c.Id, (Select AccountId, CreatedById, CreatedDate, WhoId, Id, OwnerId, Subject 
										From ActivityHistories Where Subject like '%KE: Autodemo%') 
										from Contact c Where c.Id =: con.Id ].ActivityHistories)
			{
				//if(task.OwnerId == '00530000001rFmIAAU' || task.OwnerId == '00530000001tz0yAAA')
				if(task.CreatedById == '00530000001rFmIAAU' && task.CreatedById == '00530000001tz0yAAA')
				{
					Test_Key_Event__c keyEvent = new Test_Key_Event__c();
					keyEvent.Account__c = task.AccountId;
					keyEvent.Contact__c = task.WhoId;
					keyEvent.Name = 'AutoDemo';
					keyEvent.Score__c = 50;
					keyEvent.Test_Key_Event_Date__c = task.CreatedDate;
					keyEvent.Test_Key_Event_Type__c = 'KE:Autodemo';
					
					for(RecordType rec : recordTypes)
					{
						if(rec.Name == 'default')
							keyEvent.RecordTypeId = rec.Id;
					}
					
					keyEventsToInsert.add(keyEvent);
					//insert keyEvent;
				}
				
			}
		}
		
		insert keyEventsToInsert;
	}

I am running into the governor limits in the execute (Too many SOQL queries: 201). I am assuming its because I have a subQuery in the for loop and because I am using Database.QueryLocator its allowing only processing data in atches of 200 but subquery is counted as another query.

My questions are :

Am I right in my presumption with the governor limits?

if yes

What is the possible solution . I am guessing using the scope param in execute batch but wont that limit the num of records queried in the start method query. I have around 500000 records returned in that query.

Whats the possible workaround solution.?