Is an "active lifestyle" enough activity for maintaining health? For example, I don't do any sports. However, five times a week I cycle to work (about 20-25 minutes one way, very slow pace), almost never take the lift and do yoga/pilates once a week. I used to go to the gym but I stopped a few months ago, because of lack of time. At first I thought I'm doing something wrong, but maybe just cycling and occasional activity is enough? I don't need to lose weight.
Good health outcomes generally come from cardiovascular exertion, I think the recommended minimum is 3x20 mins /week. Your slow cycle to work is better than nothing but I'd suspect your heart rate isn't elevated much. The stairs probably does raise your hr, but not for long. There are hormonal benefits of lifting weights and a multitude of health benefits from achieving regular intensive cardio. Is it enough to maintain your fitness level, well, that depends on how fit you are. The fitter you are the harder you'll need to work to maintain it. Turn that bike ride into something that gets your heart rate into the 70% of your Max and it might be.
If you are able to be active without working out, you should be able to maintain your health. You might have heard about the Blue Zones (regions of the world where people live long lives), their inhabitants do not go to the gym for workout. However, their lifestyles are very active. A lot of their activity has to do with things like farming, gardening, walking up and down the hills, etc. In other words, humans were born to move, walk, carry different weights - and this is all makes a natural workout. If your lifestyle is active enough, I guess you could go without working out in the gym. However, if like most people you spend hours at the desk, then incorporating an actual workout routine is a necessity.