Going by the warranty label, it looks to be ok (looks identical to the one on my LVW-1105HC+). Generally if a warranty label is removed, the word ‘VOID’ will become visible several times through the white middle part of the label.
With a manufacture date that old, be sure to keep your receipt of purchase as this is generally more important than the date of manufacture. Generally a warranty on most products starts from the date you purchased the product, so if let’s say you bought the DVD recorder in September, then it should be covered under warranty until the same date in September next year. However, should a fault develop, you will likely need to go back to your shop along with your receipt.