エラーがでないのでいけるかなと思ったけどやっぱり無理

type
TStageScore = Record
private

FTileCount        : Integer;

FWordPoint        : Integer;
FItemPoint        : Integer;

FIsCleared        : Boolean;
FIsOnTime         : Boolean;
FIsNoDeleteItem   : Boolean;
FIsNoUndo         : Boolean;
FDoubleUpItemCount: Integer;

FIsStageFinished  : Boolean;

function getStageScore: Integer;
function getBasicPoint: Integer;

public

CompleteWordArray: TWordArray;

procedure Init(aTileCount: Integer);
procedure Assign(aStageScore: TStageScore);

// 受信系
procedure AddCompleteWord(aWord: String);
procedure AddItemPoint(aPoint: Integer);
procedure ClearedStage(aTimePoint: Integer);
procedure GiveUpStage(aTimePoint: Integer);
procedure BreakMoDeteteItem();
procedure BreakNoUnDo();
procedure UseDoubleUpItem();

Property WordPoint        : Integer read FWordPoint;
Property ItemPoint        : Integer read FItemPoint;
Property TileCount        : Integer read FTileCount;
Property IsCleared        : Boolean read FIsCleared;
Property IsOnTimet        : Boolean read FIsOnTime;
Property IsNoDeleteItem   : Boolean read FIsNoDeleteItem;
Property IsNoUndo         : Boolean read FIsNoUndo;
Property DoubleUpItemCount: Integer read FDoubleUpItemCount;
Property IsStageFinished  : Boolean read FIsStageFinished;

Property BasicPoint       : Integer read getBasicPoint;
Property StageScore       : Integer read getStageScore;

end;

type
TGameScore = record
private
//  FItems: array of TStageScore;
function getItem(aIndex: Integer): TStageScore;
procedure setItem(aIndex: Integer; const Value: TStageScore);
public
FItems: array of TStageScore;
// 初期化
procedure Init();
procedure Assign(aGameScore: TGameScore);

function AverageScore(): Single;
function AverageWordLength(): Single;
function CountWhereWordLengthIs(aWordLength: Integer): Integer;

function GameScore(): Integer;

Property Items[aIndex: Integer]: TStageScore read getItem write setItem; default;

end;

修正後
FItems を public にした

type
TGameScore = record
private
public
Items: array of TStageScore;
// 初期化
procedure Init();
procedure Assign(aGameScore: TGameScore);

function AverageScore(): Single;
function AverageWordLength(): Single;
function CountWhereWordLengthIs(aWordLength: Integer): Integer;

function GameScore(): Integer;

end;