it's not about parsing the phrase, it's just another sense of the word beg.
6. To take for granted without warrant; esp. in to beg the question: to take for granted the matter in dispute, to assume without proof.
1581 W. Clarke in Confer. iv. (1584) Ffiij, I say this is still to begge the question. 1687 Settle Refl. Dryden 13 Here he's at his old way of Begging the meaning. 1680 Burnet Rochester (1692) 82 This was to assert or beg the thing in Question. 1788 Reid Aristotle's Log. v. §3. 118 Begging the question is when the thing to be proved is assumed in the premises. 1852 Rogers Ecl. Faith 251 Many say it is begging the point in dispute. 1870 Bowen Logic ix. 294 The vulgar equivalent for petitio principii is begging the question.