I play or have played the games you mention on a 2010 baseline MacBook Air, which sports a whopping 2 gigs of RAM, a far inferior integrated graphics card to yours, and much less hard drive space (64 gigs). Assuming you have a standard spinning HDD model, the only thing I have that is improved over your unit is my SSD. I play these games just fine on lowest settings and get decent framerates. For the record, I have also installed and successfully played Guild Wars 2 on it.
Naturally, my 2011 15 inch MacBook Pro that I've outfit with an SSD drive and maxxed the RAM blows it out of the water in terms of framerates and higher settings, but the game is certainly playable on the Air. I'm confident that any flavour of Mac built within the last couple of years will have no problem running Blizzard games. How well it runs largely depends on the unit. Obviously, the models with dedicated cards are going to outperform, but the integrated cards are getting really decent these days.
I think gaming is this is the one area Apple has downplayed in its' computer line far too long. They are certainly capable of doing it, and the popularity of gaming has risen substantially. In terms of wrecking your computer... as the first responder says, your computer was designed to be used, and Apple computers are designed for people doing very robust things with their computers, like graphic design, photography and video production. That said, I think it's safe to say that games are no more or less "harsh" on your system than these activities unless you abuse your system intentionally.