Where does the hose in that image currently go? Is that an existing dishwasher inlet or does it go somewhere else like a laundry closet or to a sprayer/sink?
Also, we need to know what type of fitting the dishwasher inlet will be. Most that I know of are threaded flex hose.
The part you show does not look like what you want, if you just want to screw it into your existing fitting. This part designed to be inserted into the middle of an ordinary copper pipe using compression fittings that join to an unthreaded copper or nylon pipe end, providing a ball-valve connection in the middle of that pipe suitable for a washing machine. You CAN use this, especially since you have a shutoff valve (which appears to have been installed in much the same way), but you must permanently alter your plumbing by cutting some part of the pipe in half to put this fitting in.
What you probably want is a male-male-female NPT equal tee or Y fitting, allowing you to screw in a second hose exactly like the one you have now. Something like this (from the same site) may fit the bill:
![enter image description here](https://i.stack.imgur.com/1AeCm.jpg)
If you can find it in nickel-steel, it'll last a little longer, but this plastic fitting should be perfectly fine. Simple, near tool-less (just a pair of slip-joint pliers or a small strap wrench to tighten down the hoses), and undoable.
It's a pretty safe assumption that the range is insulated. Otherwise it would not only pose a fire hazard to your walls and/or cabinetry, but would melt the insulation on its own wires. If it weren't insulated, it would also potentially melt linoleum flooring.
For extra safety, you could run braided metal hose, but I'd mainly consider that because it would be safer against abrasion.
Best Answer
You could potentially use push to connect fittings like sharkbite fittings. Some tools will still be required. If copper pipe is present then you need a copper cutter like the Ridged 118, if it's pex you need a PEX cutter. You can pick up all these tools at Home Depot and the like. You'll probably want to get a pair of Channellock pliers or splurge and get the Knipex Cobra pliers. You'll possibly need some electrical tools and need to do some drain work.
Make sure to turn the power off and the water. If you don't already own some of these basic tools it may be more expensive to buy them than to call a plumber, unless you can borrow some.
Push conections work on both copper and PEX and you may find a push to connect adapter with the dishwasher end ready to go. I do believe they sell a dishwasher kit that has much of the required material.