Why is Cyrano de Bergerac considered to be written in the Restoration Baroque style?
Rostand's Cyrano de Bergerac is one of my favorite plays, though I must confess I've never particularly tried to categorize or classify it by theatrical style. I'm not a theatre aficionado, either, so I had to go look a bit and see what the term used in your question, "Restoration Baroque," actually means. (My reference sites are listed below.) Even after reading, I'm not so sure I totally understand the term--or should I say two terms which are not always used together.
From what I gather, Restoration drama generally has a strong, decisive hero who is honorable and brave. Restoration comedies, however, have heroes who are rather "loose" livers who have no compunctions about flaunting moral codes. Cyrano has both. Think of DeGuiche who is so very overt in his intentions to bed Roxane; he is the anti-hero in this play. Cyrano, however, is bold and brave in every way, symbolizing the attempt of Restoration theatre to epitomize the ideal king (which they certainly had not had in the years preceding the Restoration period).
Baroque is a theatrical style which borders on farce; it's extravagant and bold and ornate. That's Cyrano himself. He's all about the grand gesture and the dramatic theatrics of love and sacrifice and even cowardice. And, of course, there is always that nose.
I suppose, then, Cyrano probably does qualify as a Restoration Baroque work. However one chooses to classify it, this is a play for all time.
Good question! You've seen that labels for large groups of works are often ambiguous. Rostand tried to imitate a style that was still just about current during the real Cyrano's lifetime (d.1655? approx - check it online). At that time poetic language was changing fast, from a 'flowery' style (full of elaborate metaphors called 'pointes' in French) to a plainer style. Some critics have claimed that the flowery style was a form of baroque, in contrast to the later, plainer style which acknowledged particular classical influences. In my opinion, there is in fact continuity rather than opposition between the two, at least where French literary language is concerned, but it takes a while to show how. If you're interested (but it's heavy going) my book Taking Humour Seriously ch. 11 has a lot of relevant material and references. I'm surprised someone used the term 'Restoration baroque': in general, the Restoration in England is more associated with the neo-classical movement, even if some aristocratic poets preferred the old style of 'conceits' (the English equivalent of 'pointes'). In France the term 'Restoration" as a literary label really doesn't apply and by the time of the restoration in England - 1660 - in France the neo-classical moment was clearly in the ascendancy and poets like Cyrano were thought hopelessly out of date. More generally, the term 'baroque' is difficult to define. If we forget about it's origin (it meant primarily 'misshapen') it was developed as a critical term first in relationship to painting and architecture, then music. When applied to literature it's not easy to transfer the visual and musical senses of the term, which are mainly concerned with lack of formal resolution. The only place where it really works is in the analysis of metaphor - check the expression 'baroque metaphor'. This returns you to the points about poetic style that I started from. Anyway, the Rostand play is nothing to do with this really - the language in the play reflects Cyrano's position as an outsider, I suppose; but in the real Cyrano's lifetime this language was considered highly appropriate for a man of the world, if old-fashioned by the time of his death.