Sort of. You can have a rule without a trigger, but it will never run unless it is manually executed (eg. from a dashboard).
If your goal is to have the rule run when any of those doors open, then you would want to add the doors to your Triggers as well. Something like the following.
*Note that the IF Condition itself was edited to change from ALL → ANY
PS. Here’s a an old post describing Triggers vs Flows that you might find helpful. It’s a bit dated in that it doesn’t include some of the newer features like HTTP triggers, but it covers the main concepts.