Running is arguably the most efficient form of cardio exercise because it’s a weight-bearing action. That is, all of your body weight is involved, so you don’t have to work as long to get a certain result. Other forms of cardio exercise — swimming, cycling, rowing — are all very good too. They’re certainly better than nothing. But you have to work significantly longer to get the same cardio-building effect. Running also strengthens your leg muscles, ligaments and tendons in a way the other exercises don’t, again because of its weight-bearing nature.
So the closest thing you’ll get to outdoor running at home is to run on a treadmill. You’d have to take the platform angle up a few degrees to compensate for the lack of resistance (ground and wind). Beyond that, skipping rope is a very good substitute. It’ll work your lungs hard and it’s weight-bearing, but doesn’t come as naturally as running. Takes practice to do well, but can be every bit as taxing on your body as running. Walking is a great weight-bearing exercise, but you’ll need to do it briskly and for 2x or 3x the amount of time to get similar results to running.
If you’re trying to prepare for military training (e.g. plebe summer), try your best to run outside. Occasionally you read stories here of a top-level endurance athlete (e.g. swimmer, cyclist) who gets to an SA and struggles with the running. Again, there’s really no substitute for the weight-bearing, ground-pounding nature of rapidly putting one foot in front of the other.