The lasing process begins when just one photon is accidently emitted. This explains why the photons on the line between the two mirrors are in phase. But what about the neighboring atoms or even distant one not on that line. How are they excited by that initial photon (by its wavefunction? WF) and why will they go perpendicularly to the mirrors. I expect they will go radially because the WF is spherical. And how does a plane wave build? The Huygens principle says that a spherical wave builds also spherical wave.
That is a good question, that can bring you much closer to understanding wave propagation.
First: waves - light waves - are not rays. They are always spread out. If you squeeze them down to a small beam in one place, they will immediately spread out over a wide angle downstream. This is directly related to Huygens Principle.
Second: in a laser, light travels back and forth between the two mirrors many, many times-- so it travels a long distance. The farther a light wave travels, the more it will spread (unless a lens or curved mirror refocuses it). So, typically one or both laser mirrors is curved to keep the beam confined. But what that means is that the light wave - the beam- occupies a volume inside the lasing medium. Every atom in that volume is influenced by the beam, so stimulated emission from all the atoms in the volume ends up in phase. See this.
As mentioned in S. McGrew's answer, the light waves do spread out. Using a low-quality laser, you can notice that the beam spreads out and becomes less intense when projected on a surface that is farther away. Waves emitted from a single source and in a single direction always radiate outwards in a cone; most lasers are just so focused that it is difficult to notice. Even with the wave-particle duality of light, we know that lasers will behave this way because we can replicate Young's double-slit experiment and create an interference pattern, wherein the waves emitted by the laser interfere with each other after being passed through two parallel slits. here is a resource which proves this.