Yes, that is the Engine DJ library software. The software of your Prime 4+ is called Engine OS. Your OS is the older Beta version, but you can update it to the latest version. There are several ways of doing this (but I don’t know if the Beta supports updating over Wi-Fi).
The following way to update the OS I know from my SC6000M players and the Live 4, it should work for the Prime 4+ too, step by step:
- Go to the download page:
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On the right side, under OS, where it says select your device, select the Denon DJ Prime 4+.
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Download the updater file, depending on your laptop, for Windows or Mac. The Windows updater file is Prime 4 Plus 4.2.0 Updater.exe, for example.
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Launch the downloaded Installer/Updater file on your laptop.
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Connect your Prime 4+ to the laptop with a USB cable. The SC6000M has a blue USB cable for this, probably it is the same for the Prime 4+. Switch on you Prime 4+.
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On the Prime 4+, swipe down the menu from the top of the screen. If you have not used the Prime 4+ so often, this may be new to you, there is a menu that becomes visible if you swipe one finger from the top of the display to the bottom. There go to Settings.
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In Settings, go to the About/Update tab. Find Update Firmware, it should have a button labelled Reboot. Tap on it. On the Prime 4+ you should now see a window asking How do you want to update? Choose Computer. And then the Prime 4+ will enter update mode, the screen will probably show a large Engine DJ Text and a microchip icon.
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On your laptop, click the Start Update button in the Installer window. While the update is being installed, do not turn off the power. After the installation the Prime 4+ reboots. And welcome to the future!

I hope that this helps you and that all goes well. There is also a helpful YouTube video, which shows the other update methods as well:
About the version numbers: The Engine DJ library software (on your laptop) is currently at version 4.2.1, the Engine OS on the players (like the Prime 4+) is at version 4.2.0.
P.s. And maybe some of the other Beta users can confirm this or correct it if something is different in the Beta version.