If a video game franchise like Warcraft, Dota, Diablo, StarCraft gets converted to tabletop RPG, will this require a license from owners if this RPG is private only?
The issue at hand is likely that of Trademarks.
Trademark law protects distinctive words, phrases, logos, symbols, slogans, and any other devices used to identify and distinguish products or services in the marketplace.
If you do not attempt to market your game, which would include selling or giving away the ruleset, material related to it, or marketing an experience with it (such as selling gaming sessions playing your homebrew Starcraft game), then trademark does not apply any more than referring to your holiday punch as "Blotto Coca-Cola" among your friends at the party.
The practical answer is that, if your adaptation is truly for private use only, then whether it's technically legal or not doesn't really matter, since you're very unlikely to get sued (or even to get asked to cease your infringement, which would be the typical first step before an actual lawsuit if someone did object to what you were doing) for two main reasons:
If your use is truly private, then no-one outside your private circle of friends — including the owners of the intellectual property that you're using — should even find out about it in the first place.
Even if your word of your "private" use got out, e.g. because you documented it online, and the owners of the IP found out about it, they'd have little if any motivation to sue you as long as you weren't making any money off their IP, competing with them, or tainting their public image with your use.
(That is, of course, assuming that you're actually not doing any of the aforementioned objectionable things. If you were e.g. distributing your game outside your private gaming group, charging money for playing it, or featuring "unsavory" elements in it that the IP owners might strongly object to, things might be different.)
Basically, your private adaptation would most likely fall into the wide legal gray area known as fan works. Most of that is not strictly legal, but there's a lot of it around anyway, and media companies and content creators usually tolerate it at least up to a point, because strictly enforcing their legal rights would cost a lot and bring little if any benefit to them. Lawsuits are expensive, and even "cease and desist" letters sent to fans can be costly, in terms of PR if nothing else. Companies normally don't waste time and money on them without a reason.
Some companies may even explicitly encourage at least certain types of fan works, and may have explicit "fan content" policies that may offer you you additional guarantees of protection beyond just "we probably won't bother to sue you." Of course, such guarantees typically come with additional conditions and restrictions, which can vary case by case, and which you'll need to research yourself.
In some parts of the world local laws may also offer some additional protection for certain types of "fair use", but again, such laws (and precedents in their interpretation) will vary between jurisdictions.
In practice, your best bet is typically to look around to see what kinds of fan works already exist for the franchise you want to use, and how far the companies owning the relevant IP (trademarks, copyright, etc.) seem to tolerate it. If you don't push the envelope in that respect — and especially if your use is indeed private and not publicly disseminated — you're unlikely to get into trouble.
And, of course, if you do receive a "cease and desist" letter, comply with it. Or, if you really don't want to, consult with a local lawyer on what other options you may have.
Technically it violates civil law, but a lawsuit is unlikely.
An adaption of a video game into a tabletop RPG is a derivative work, which falls under copyright law. I am not a lawyer, but here's what Wikipedia says:
In the United States, according to 17 U.S. Code § 106, the copyright holder has exclusive right to prepare derivative works based on a copyrighted work. This is a civil offense; i.e. Activision Blizzard would have grounds to sue you.
To count as criminal copyright infringement, it would have to be shown that you wilfully infringed on for the purpose of commercial advantage or private financial gain. It would also have to be on a substantial scale, i.e. over $1,000.
There is an exception to copyright known as Fair Use, but it only applies in limited situations, and the definition is somewhat subjective. It may count in your favor that it does not impede Blizzard's ability to make money from their own work, that you only used a limited amount of copyrighted material, and that your RPG is not a commercial product.
Of course, it's highly unlikely that Activision Blizzard will actually sue you over a private tabletop RPG group.
Ilmari Karonen's answer seems the most practically applicable.
I just wanted to address a point that wasn't addressed yet by any of the existing answers. Sean Duggan mentions trademark, but trademark is far from the only thing you need to pay attention to. Copyright is extremely relevant, and you do not have to be involved in the marketplace to violate copyright law: non-commercial uses can infringe copyright.
An adaptation from one medium to another is a clear-cut case of a derivative work. Therefore, you are practically certain to infringe copyright if what you mean by "converting" is using the world or any of the specific characters or entities found in the video game franchise.
Copyright does not cover ideas, only their expression, but if the aim of your project is to convert a video game franchise to the tabletop RPG format (rather than something like "creating a tabletop RPG with the feel of this video game franchise" or "that has similar gameplay to this video game franchise") it is probably likely you will infringe copyright even if you avoid the use of any trademarks.
Some relevant former questions: