You know when you do a speed test and it tells you your Mbps? I wouldn't be getting a full Mbps but 7/10 of one. Which isn't a lot of bandwidth at all. I'm thinking some games must use at least 3-5 Mbps to be playable. And maybe in games like WoW when I'm around a lot of people it may not be able to handle it. But this is all just me speculating I have no idea.
That is bits, and it depends on the specific game but usually games do not need a lot of bandwidth [to play] and are more about latency, patch day is going to suck however at that speed. No gaming developer I have ever seen has decided to lose its dsl customers to date by making on line play too bandwidth intensive, you may however have to turn down/off some game effects and lower quality to keep data transfer to a minimum.
Where the bandwidth will be a problem is if you have someone else use the internet to say stream you tube while your trying to play then the lack of bandwidth is going to kill you, but if you get all 700 Kbps you should be good. Only one way to find out though, try them.
When wow first came out I played it on a dial up connection, then later a712Kbps dsl connection. its was noticeably better on dsl. However, even on my 100 Mbps cable connection[after I moved] the game did not play better network wise except that multiple things could be done and I did not notice where as on dsl if someone watched a video it woudl kill me and I mean a 320x200 slide show would even axe my game play].
Though there have been a number of Xpacs since then and the data requirement may have changed, I suspect if you turn down and/or minimize the game effects [ie have low quality audio, video, no extra effects, kill the friend app, don't try to use voice chat, etc...] you will be ok. You may be able to use the voice chat, voice uses barely any bandwidth in reality, but you'll have to test that.
Blizzard has pretty much just always said a broadband connection and dsl used to be considered broadband, since the FCC has changed the definition over the years your 700 Kbps is no longer considered broadband.
If you can get 4G/Lte service where you live it may provide an alternative for gaming but DO NOT download patches over it or they will throttle you rather quickly [in the USA at least]. I just ran metro PCS [personal] and verizon [work] lte/4g tests and I get 8.6 Mbps on one, and 4.7 Mbps on the other, your mileage may vary but latency was rather high IMHO. 82ms Verizon, 200ms metro a state away but again this is to a speed test site not known for being optimized for latency like games are.