The modern meanings were around in Shakespeare's time, but lacking the modern dramatic nuance we find when referring to adventure comics, adventure stories and the like.
Most Shakespearian uses have a more general sense of venture, enterprise or the outcome of a venture. When Hotspur talks of "the adventure of this perilous day" (Henry IV Part 1, V.ii.95), he is not thinking primarily of the excitement involved in the battle. Other fights, similarly, are referred to in terms of "adventure", as when Lewis the Dauphin talks of "the fair adventure of tomorrow" (King John, V.v.22). And when Warwick talks about his scouts getting into the enemy camp, he says they "found the adventure very easy" (Henry VI Part 3, IV.ii.18), by which he means simply the "enterprise".
Rosalind is the only one to use the word in another general sense, of "experience, fortune, chance", when she says to Silvius, "searching of thy wound, I have by hard adventure found mine own" (As You Like It, II.iv.41).