document.OA1.Open( “c:\\2007-07-3121.02ChatLog.rtf”, “Word.Document”);
var objWord = document.OA1.ActiveDocument;
var objRange = objWord.Range();
var count = objRange.ComputeStatistics (0);
window.alert(count);

The follow is a vbscript to get the line count.

Set objWord = OA1.ActiveDocument
Set myRange = objWord.Range
Dim WordCount
WordCount = myRange.ComputeStatistics(1)
MsgBox WordCount & ” words”

About the ComputeStatistics method.
Returns a statistic based on the contents of the specified range.
Constant value:
wdStatisticCharacters 3
wdStatisticCharactersWithSpaces 5
wdStatisticFarEastCharacters 6
wdStatisticLines 1
wdStatisticPages 2
wdStatisticParagraphs 4
wdStatisticWords 0