To automate all things on my Droids, I use Tasker1. Like Steve with IFTTT, I didn't check with your specific situation – but given the fact that Tasker is the most powerful automation tool available for Android, I trust it to be capable of this. Tasker works with so-called "profiles", consisting of a (number of) "conditions", which you can assign "tasks" to. WiFi is one of its easiest tasks ;)
Tasker with the Motion Detection addon (source: Google Play; click images for larger variants)
So let's check how it goes with your requirements:
- Automatically disables Wi-Fi when movement is detected: Tasker can react on a lot of things, amongst others Sensors. Unfortunately, it doesn't ship with movement detection built in – but there's the Movement Detection addon available to fill this gap (see screenshots above).
- Automatically re-enables Wi-Fi when the device stops moving: By default, Tasker automatically reverts to the "before-state" whenever a condition is no longer met. You also can define exit-tasks, so to make sure you could place the "turn it back on" here.
- Compatible with Android 4.4.2: I have no device to check, and Play simply says "varies with device" – but considering how actively Tasker is maintained, I'd say yes.
- Ability to set a triggering speed threshold: Certainly to a degree at least, as Android gives this in different categories like "walking", "cycling", "car" – which match "different speeds".
- Ability to have different profiles for different moving speeds (walking, jogging, driving): Ahm... see previous bullet-point: Yes.
- Allows a small time window before triggering (walking a few steps across the room should not disable your Wi-Fi): Yes, the mentioned add-on has that configurable.
- Pop-up notifications whenever Wi-Fi is switched on/off: Not by default, but you can add this to the task. Tasker can do popup-notifications, toasts, or put stuff to your notification bar – so chose what you like. You can also have a notification with audio-alert ;)
- Reasonable price: Well, that's a little subjective. I'd say for what it does the price is reasonable :) OK, facts: Tasker costs about US$5 (they have a free 7-day trial on their site, which easily can be extended for another 7 days2 – so you can "try before buy"). The Motion Detection add-on adds another buck to that.
As I wrote, Tasker is well maintained. There are tons of add-ons available to extend its functionality, and many apps directly support it (so you can automate them using Tasker: I e.g. control FolderSync this way, to sync certain stuff only on given conditions). For a list of tutorials, addons, supporting apps, and more, be welcome to see my Tasker Resource collection.
1: Link goes to the Tasker Tag-wiki at our sister site for more details
2: Export your configuration, uninstall Tasker, re-install Tasker, import your configuration