Does the entire blockchain have to be recomputed to validate a transaction? Are transactions validated by recomputing the entire blockchain? If not, how else can it be confirmed that a bitcoin I'm attempting to transact is one that I actually had come into acquisition of previously and still have?

If yes on the other hand, how long does that recomputation typically take in practice, and does that pose a scalability risk in the potential for Bitcoin usage (and hence the length of the blockchain) to outpace Moore's law?
No.  The blockchain must be queried, but not recomputed.  If you see a transaction that has two inputs, you will need to query to check if those outputs have been spent.  You will also need their encumbrance scripts in order to check the spending transaction meets the required criteria.  In essence, this is just a database lookup.