There is an expiry date, it should be printed somewhere on the packaging. One of the advantages of buying in store is the ability of looking at the expiry dates and buying one that has a few years left on it.
How long do they last? Depends on how long it was sat on the shelf before you bought it. Old stock might have already expired or have less than a few months. Newer stock should have 2 to 3 years on it. From what I understand the kit you reference leaves the manufacturer with 3 years on it. Some of the individual tests leave the manufacturer with 4 years. The nitrite test will last longer than the nitrate test for instance.
Should it be thrown out? They will become more unreliable the older they get. No guarantee that a test kit within the expiry date is going to be reliable, especially if it's not been stored in suitable conditions. It's a home test kit, not laboratory testing. If you are doing a single test and you have no reason to suspect anything is wrong, but just want some surety, I wouldn't buy a whole new test kit. If you have reason to think something is wrong, but your test kit says there is nothing wrong, you might want to get a new kit to make sure. If you are regularly testing I would always use an in date test kit.