I think this could do the job...

set nocount on
SET ROWCOUNT 1000

declare @rowcount int, @batchcount int, @rowsupdated int
declare @LastKey nvarchar(341)
select @rowcount = 1,@batchcount = 0, @rowsupdated = 0, @LastKey = ''
while @rowcount > 0
begin
  begin tran
     update MyTable
     set NewZip = ZipCode,
          @LastKey = NameKey
     where NewZip is NULL
        and NameKey >= @LastKey
     set @rowcount = @@rowcount
     select @rowsupdated = @rowsupdated + @rowcount
     if @rowcount > 0 select @batchcount = @batchcount + 1
  commit
end

Ians, I believe you can use it for production.

The last value assigned to @LastKey is the largest NameKey in the set because the update query definitely uses the index [LargeTable__IE1].

You are actually both right.

But just to make sure of this behavior, you can use an index hint in the query.  This pretty much guarantees the results.