From your questions it seems like you are wondering how to connect this.
As in: "It requires a type A port I am not familiar with this type port"
"Do I need to purchase an adapter"
A "Type A" (and you didn't mention that you were inferring it was the USB Type A) is your most common of USB connections. The other, the Type B, is most commonly used on the back side of peripherals, like printers and scanners. Hooking up USB devices to your computers ports usually just involves the Type A. But whichever type is required, you just use it. If it plugs in, you use it.
I have checked out that IoGear KVM, and there is nothing unusual about it. The cables needed to connect to either of the two computers are fast-molded onto the KVM. Just plug those sets into their respective computer. Your current USB mouse and keyboard just plug right into the open ports of the KVM switch. And finally your monitor plugs into the 15-pin VGA connector. What's so hard. Just try it.
The worst problem you MAY have, might be with the one computer that has PS/2 keyboard and mouse connectors along with the USB. Some of the older computers (and I do not know about the Dell Dim L800R) don't immediately recognize the USB ports until Windows is up and running. If that is your case, you will only have a problem with trying to press a special key sequence in trying to get to the BIOS setup of that computer. That is because if the USB ports are not available until Windows is running, then how can you do a key-press with a USB keyboard to get to a point before Windows is running? IF THAT is your case, just plug a PS/2 keyboard in during those few occasions where you need to get into the BIOS. Otherwise, don't worry about it.
In answer to trying any USB-PS/2 adapter ... DON'T do it. Not only is it not needed for your setup, it will probably only overly complicate your setup.
I have a 2 port KVM with audio pass-through here, myself. It is a cheap AirLink brand, and only one of my computers connected has the PS/2 connectors. But I have no complications with getting to the BIOS in either computer.