So, typically the washing machine drain hose is just pushed into the drain in the laundry room, and often there is a clip to hold it curved so that it falls in place. They’re generally not sealed into place. Sometimes the end is ribbed to hold it into place.

In your case, it appears that you have the ribbed end type that someone put into a standard drain fitting that uses a compression ring/collar to seal. Your hose end technically wasn’t made to fit that, but it doesn’t matter, because you just shove it in and it wedges in place. The problems come when vibrations due to the inherent load imbalance from washing clothes rocks the washing machine, wiggling the hose, and over time causing it to come loose.

In your case, you just shoved the hose back in, which is reasonable and what most people would do. While this may work indefinitely, there is also a possibility that it could work loose. To prevent this, you might change the hose end fitting to more securely lock into place, use silicone caulk to glue it into place, or, if it is reasonably secure as is, simply use some zip ties to tie the grey washing machine hose to something like the black line coming in above. That way, when the machine vibrates, the pull on the jiggling hose doesn’t reach the hose end connection and loosen it.