Most laptops (and even desktops now) use a mini HDMI connector, but according to Acer's website the laptop uses a normal full size HDMI connector, so it should be fine.
HDMI is a passive cable, meaning that it merely connects controllers on either end of the wire. The only difference between an HDMI cable that runs HDMI v1 or HDMI v1.3 is the quality of shielding and capability to not pick up interferance. Most old HDMI cables work perfectly fine with the newer standards over short distances (3 feet or less), and it tends to only be over longer distances that the cable rating matters. If you have a sub-par cable then it will still work for older stuff (like 1080p display with audio), but simply will not be able to support the bandwidth for newer features like 60fps video, 3D video, or resolutions much higher than 1080p.
In other words, for basic display purposes; If it fits, then it works.