Question: Is it because it is a non-approved app on iPhone 4 and why? If so, is it only installable if it is a jailbroken iPhone 4?

Answer: 
The previous free Siri app for iOS was removed from the App store sometime around Oct 4. (A developer can remove an app of theirs from sale at any time, and Apple purchased the developer of this app.) This app (for people who downloaded it before its removal from the App store) itself announces that it will stop working on Oct 15, most likely because the old servers for its messy protocol will be taken down. So the old Siri app will most likely stop working even if someone is able to install it.
There are stories in the blogosphere that hackers have migrated Siri from the 4s OS code onto an iPhone 4. There was a video demonstrating it.

It's not for the masses. In fact, it had some substantial problems.

There was a story a day or two ago that Apple is working on releasing Siri for older phones (the story said iPhone 4 and maybe 3Gs). Then a story yesterday said that's not the case.

If you're Apple and you've just released a phone that is all new on the inside but looks the same on the outside, and has this one killer feature that revolutionizes everything... would you be in a hurry to put that feature on older phones? I wouldn't. You'd gut sales of your new device. You *might* bring that feature to older devices in maybe six months or something, but you'd for sure let it be a unique draw to your new device for a good while.