Yes. Readied or not, movement is movement.
The definition of "movement" in the rules doesn't change based on whether it's done on your turn or someone else's. The rules don't say that if you move on your turn, it's considered "your move", and that it's called something else if you move on someone else's turn. It's just that you don't normally have a pool of movement to use outside your turn unless you take the Ready action.
From the "Movement and Position" section:
On your turn, you can move a distance up to your speed. You can use as much or as little of your speed as you like on your turn, following the rules here.
The Ready action says (emphasis mine):
Sometimes you want to get the jump on a foe or wait for a particular circumstance before you act. To do so, you can take the Ready action on your turn, which lets you act using your reaction before the start of your next turn.
First, you decide what perceivable circumstance will trigger your reaction. Then, you choose the action you will take in response to that trigger, or you choose to move up to your speed in response to it. Examples include "If the cultist steps on the trapdoor, I'll pull the lever that opens it," and "If the goblin steps next to me, I move away."
In addition, consider that things like the rules on difficult terrain state:
Every foot of movement in difficult terrain costs 1 extra foot.
If the term "your move" or "your movement" only applied to your turn, then difficult terrain would somehow impede regular movement on your turn but not impede readied movement. This is clearly illogical.
...But features related to your move might separately restrict timing
Some of the things dependent on your movement may also specify whose turn that movement must be on. For instance, the "Other Activity on Your Turn" section that you quoted specifies, in addition to the name of the section (emphasis mine):
Your turn can include a variety of flourishes that require neither your action nor your move.
The options specified in this section relate to what can be done during your turn. Even if you want to do some other activity as part of your move (e.g. interacting with one object or feature of the environment), you can only do it as part of your own turn, not as part of your readied movement. For more details, see:
Naturally, DMs may choose to allow these as part of readied actions at their discretion, but the rules clearly delineate them as "other activity on your turn".