Even though alcohol-free weddings are fine, and you certainly have a valid reason for wanting one, it always hits me wrong when someone says the reception "is about us and not them". Actually, it's the opposite. The reception is to thank your guests for being part of your day, so it's about THEM, not you. I'm hardly saying serve alcohol, but rather don't go around stating it this way.
You're smart to aim for a wedding earlier in the day, but then when you mention a "cocktail hour", I guess I read that wrong. Have you considered a luncheon wedding or a brunch type one? Don't do this if you don't like the idea, but it might make it easier.
On the board games, if you're sure everyone invited would love to see this, it might be ok, but overall weddings don't usually go overboard to compensate for not serving alcohol. I go to weddings to visit with people I haven't seen in awhile, not play board games (and I love board games! Just not at weddings).
Also, if there are any guests you think might be rude enough to bring alcohol into an alcohol free wedding, this is unbelievably crass. Your options are to not invite them, or else make it clear ahead of time that they will be escorted off the premises if this happens. Another way to handle it is pick a venue that doesn't allow alcohol. Lots of them don't, and then it becomes not only a social violation, but a legal one, as well.
PS - @cammie, sorry to butt in! But I'm a substance abuse counselor and what you say isn't always true. I've known people 30 years sober who still avoid any situation where alcohol is present. The important thing is for the person to identify slippery places and people, and her fiance has done this. It needs to be respected, and that's why it's so unconscionable that some guests might bring alcohol into the wedding. Personally, I would tell them our relationship/friendship is over if they do something like that.