Kindle Fire HD 7" runs very slowly after rooting
The process of rooting your tablet shouldn't affect the performance.  However, any apps that are installed when rooting can affect the performance.  SuperUser is a very common and popular app that is used when rooting and I have not seen any performance impact when installing SU on Motorola and Samsung devices (100+ devices).  

Based on the junk that the first link tried to get me to download and how my virus detection (AVG) went off after extraction of the Zip, I'm guessing that there could be an app that was installed when rooting the tablet that could cause some performance delays (adware, monitoring app, etc.).  It's an extremely large download to for just rooting a tablet and the fact that it has 2+ threats to security programs it's not a good sign.

You can look at apps that are taking up system resources by enabling Developer Options and then looking at "Process Stats" under Settings->Developer Options->Process Stats.  This will show you what apps are taking up a lot of CPU Cycles.  If there is something you don't recognize and it's not a Google service, it could be something that was installed when rooting and soaking up resources, slowing your system.  

The .bat file in the second download (Qemu) looks legitimate and there is nothing malicious in the batch file.  

You can try uninstalling Superuser.apk from your device and installing it from another source.  This could resolve the sluggishness you tablet is experiencing.  

Before doing anything else, I would recommend doing a complete backup of your entire tablet so you have a restore point if anything else goes wrong.  I use TWRP on the devices I manage and I've had excellent experience with it.  It appears they have a version for the Kindle Fire XDA Link.  If you already have a way to backup everything from the system level, use that before installing/uninstalling anything else.