Short answer: no, it's not an SLR. It's what is typically called a "bridge" camera, or superzoom compact.
The description of an SLR camera is in the name - single lens reflex. An SLR is defined by having a "reflex" mirror inside the camera body. When the shutter is closed and you are looking through the viewfinder, this mirror is down and redirects the light coming into the lens up towards the viewfinder.
When you take a picture, the mirror flips up, clearing the way for the light entering the lens to travel onto the sensor or the film.
An SLR typically has other features. All SLRs that I know of have interchangeable lenses (although I guess this isn't strictly required). They have some arrangement of prisms or mirrors inside the viewfinder that corrects the image from the mirror. SLRs historically have larger sensors than most other digital cameras, although this is no longer the case.