I think a lot more longbow shooters use arm guards than recurve shooters, for two reasons. First, as Dennis mentions, longbows are usually braced lower than recurves. Second, more longbow shooters hold the grip fully in their hands, as demonstrated by Kirk in the video. Both of these make it more likely that the string will slap the forearm. Neither of these are bad, per se, and most of the top longbow shooters do use arm guards.
If you are shooting a recurve braced at 8" or more, and gripping the bow with the offset grip demonstrated by Kirk, you shouldn't be slapping your forearm, anymore than a compound shooter. If you are, you may be either gripping the bow too far into your hand, past the lifeline, or not rotating your elbow out of the way.
Or, you could be hyperextending your elbow, rare in men, but common in women. If that is the case, you may have to get used to shooting with a slightly bent bow arm.
Some shooters always wear armguards, whether they need to or not, just to keep their shirtsleeves or jackets out of the way of the string.