became confused when doing first 360 licence transfer

Sorry, but you will need to work with support for them to do a manual transfer (they can in certain circumstances). They are the only ones who could do so.

Digital Rights Management (DRM) technology is used by content providers, such as Xbox Live, to control how digital game and video files are used and distributed. Xbox Live sells and rents DRM-protected videos, games and add-in content that are covered by
media usage rights that allow specific uses of that content.

When you purchase content, you receive a licence to use that content. The licence has two parts: the system licence and the local licence. The system licence applies to the gamertag that purchases the content, and the local licence applies to the console
where you first downloaded the content.

Transfer content licences

You can transfer content licences from one console to another once every four months.

If your console was recently repaired, or if you’ve purchased a new console, use the licence transfer option on your console to transfer content licences. Here’s how:

1. On your console, sign in to Xbox Live using the gamertag that you used to purchase the content.
   
2. Go to the Settings and then select Account.
   
3. Go to Your Billing Options, and then select Licence Transfer.
   
4. Follow the on-screen instructions to transfer the content licences.
   

After the licences have been transferred, you need to download the content again to update the local licences. This way the content can be used by other profiles on your console and when you’re not connected to Xbox Live.

This is only for the 360 and does not transfer anything between accounts.

When you purchase content, you receive a licence to use that content. The licence has two parts: the system licence and the local licence. The system licence applies to the gamertag that purchases the content, and the local licence applies to the console
where you first downloaded the content.

Transfer content licences

You can transfer content licences from one console to another once every four months.

If your console was recently repaired, or if you’ve purchased a new console, use the licence transfer option on your console to transfer content licences. Here’s how:

1. On your console, sign in to Xbox Live using the gamertag that you used to purchase the content.
   
2. Go to the Settings and then select Account.
   
3. Go to Your Billing Options, and then select Licence Transfer.
   
4. Follow the on-screen instructions to transfer the content licences.
   

After the licences have been transferred, you need to download the content again to update the local licences. This way the content can be used by other profiles on your console and when you’re not connected to Xbox Live.

It may be to do with content licences. Have you signed in to Xbox LIVE on your new 360 since transferring your content yet? You will need to sign in to Xbox LIVE to associate your content to your new 360.

If this doesn't work, you can try and run a Licence Transfer by following these steps:

1.Sign in to Xbox LIVE using the gamertag that you used to purchase the content.

2.Go to Settings and then select Account.

3.Go to Your Billing Options, and then select Licence Transfer.

4.Follow the on-screen instructions to transfer the content licences.

Content licences are for every downloaded item, not just Arcade games.

How you do a license transfer is in the link OwenKiller already posted, under the heading "Can I transfer a content licence from one Xbox 360 console to another?".