No, its still an 'or else'.
An unmarried couple *do not* spend time together like that unsupervised. Doing so among noble classes is how you start grudges.
In this case its less of a shotgun wedding and more of a "You've been spending this much time with my daughter so clearly you intended to marry her. Right?"
Sneaking off with an unmarried Heir is a biiiiiig no no. Like "There may be well be war for this."
It was still incredibly improper for you to have done so, but by agreeing to marry you remove most of the downsides from your bad manners.
In fics where Hiashi pulls this on Naruto and Hinata its usually fairly good natured, him 'demanding' they marry is actually his way of showing approval. Both kids get what they want, and he gets to see his daughter happy, without compromising the hardass clan elder role he has to play. He doesn't have to demand marriage, if he was actually pissed he could demand punishment/compensation instead.