Earlier quoted context omitted.
The Gaussian mixture representation is quite interesting, so thanks for the link. But it seems like they do not make use of the relative position of words in the text either. They simply maximize the margin of the expected likelihood for words that occur in the same context over those that do not. However, in most cases it's probably actually better to ignore word order, since that captures more semantic relatedness…
Whether it's okay to ignore word order really depends on your goals. In my work, tracking word order to build a sentence representation is necessary to get composition rules correct. You can get away with ignoring order surprisingly often but when it's needed, it's vital. When aggregated across an entire corpus, order ends up mattering a lot, in an absolute sense (something looking only at accuracy numbers will hide)…
When you want to handle whole sentences, obviously order becomes much more relevant, but for that you'd feed the word vectors into an LSTM or similar to handle the order-dependence.