So, why is the gift balance still in Blockchain Wallet when I log in to their site?
Because blockchain.info still has the private key associated with that address.
When importing into MultiBit, did I not transfer the funds out of Blockchain?
No, you did not.
Wallets are a collection of private keys (you can think of them as passwords) that allow you to transfer value to the control of someone else. The value itself is actually stored in every instance of the bitcoin blockchain that every full node maintains a complete copy of. When you create a transaction, you use the private key to provide proof that you are authorized to reassign that value to the control of someone else and this proof is stored in the public blockchain.
All you've done by exporting and importing is created an additional copy of that private key. At this time either wallet (MultiBit or blockchain.info) could create a transaction spending those bitcoins.
Is MultiBit simply showing the combined balance of multiple Keys, but not actually combining them into one wallet?
As I stated, a wallet is a collection of private keys. The wallet software uses its knowledge of those private keys to look up all the values associated with all the keys. It calculates the sum of those values and displays that to the user so they know the total value that they have control over with that wallet. Each and every transaction is separately maintained. The only way to "combine" the values is to create a transaction that sends the combined values to an address.
If so, how do I now remove the Blockchain Key, so I can then simply transfer the funds to MultiBit wallet?
It would have probably avoided some confusion if you would have just used the blockchain.info wallet to create a transaction to send the value to one of the addresses listed in your MultiBit wallet. To reduce future confusion, you could use your MultiBit wallet to send your entire balance from your MultiBit Wallet to one of your MultiBit wallet addresses. This chould combine all the unspent outputs that you control into a single new transaction output all stored associated with that single address.