Most Westerners, I think, would contrast "religion" with "philosophy", "rationalism" or "science". When we do that, Buddhism as practised in traditionally Buddhist countries (and mostly as practised in the West) doesn't fit neatly in any single category.
Religion is typically devotional, science isn't: devotional practices are common in Buddhism but are not encouraged in the suttas.
Science is always open to debate and improvement, religion isn't: many Buddhists would say that the suttas are the first and last authority.
Science is systematic and analytical, religion is mystical and non-rational: Buddhism has elements of both.
... and so on.
However, I have to say that Goenkaji's arguments for the non-religiosity of Buddhism are fairly weak. Saying that the word "Buddhism" (or any related word) was not part of the dharma is no proof that the teachings didn't add up to "Buddhism" in the religious sense. As we say around here, if it walks like a duck and quacks like a duck, it probably is
[Edit: this is just another away of saying what Bhikku Pesala has just said, "Avoiding words like "Buddhism," "Buddhist," "Converting," or "Religion," are mere sophistry..." ]