Does this sentence mean something like "Mary plays double" or "Mary plays a double game"?

It means that she has (she's dating with) either two boyfriends or two girlfriends or one boyfriend and one girlfriend at the same time.
So it means basically the same thing as メアリーには恋人が2人いる.

So, 「二股をかける」 always bear a, say, "sexual" subtext? Or does this subtext appear only in certain context?

I think so. At least I think I never use it for other meanings.
I'm not really sure, though. It seems it's a little different from what dictionaries say.

> It seems it's a little different from what dictionaries say.
That was the reason why I asked :-)
Thanks for the explanation, Tommy!

I agree with tommy_san.

I believe "二股をかける" is usually used for lovers, such as girlfriends and boyfriends.

Thanks, bunbuku-san!
By the way, is it possible to use this expression talking about an adultery, too?

I think we would use 浮気する or 不倫する for that.

分かりました。ありがとうございます。＾＾