Well, it depends. When the biggest measurement on the chain stretch tool says it's time for a new chain, then the chain is really dead (and possibly your cassette too). It's not a bad idea to change the chain when the shorter measurement side falls through, especially if you're experiencing shifting problems.

I would look at the cables, too, though, because those will often just last a year, while a lot of chains will go a bit to a lot longer than 1600mi. Chain life will depend on your maintenance habits and riding style. You could wait until your cable goes to the point where you keep losing a lot of tension and have trouble shifting anywhere but into the little ring. Try a front derailleur cable indexing tune up. If the tune helps, then that might mean that your cable is getting old (and the problem might resume). If it doesn't help, then it is more likely your chain and the strain put on it when you crosschain.