No, not really. I do think that urls that use [topic].forum look nice and sleek, but it isn't something that has caught on with major popularity. Many people still look for .com's and even sometimes enter it automatically. I do think it has its uses, though. Especially for big popular topics. For example, a forum about call of duty could use callofduty.forum or a forum about first person shooters could be fps.forum or something. Those bigger, more popular categories can really take advantage of these extensions the best in my opinion.
Eh not a huge fan of .forum or .community, just prefer the traditionals like .com, .net,.org, etc over individualized domains. I think for some communities with unique names/niche it could work well for them, but you'll figure out if the site is a forum/community once you visit the link.
I don't think he's looking at purchasing one or the other, I think this more of an opinionated question, rather than "should I buy this for my forum." That said, I don't think I'd choose either option, although .community looks like it could be a solid choice for a general discussion forum. However, like most people, I too prefer the traditional domains