I focused on copyright and cyberlaw when I obtained my JD, but I never took the bar because I knew I didn't want to practice law. So this is backround material, not legal advice, and I am not a lawyer.
There are two legal areas to pay attention to here: trademark and copyright. Trademark was created to protect businesses from fraudsters trying to masquerade as them: "Hey, trust us, there's an Apple logo on that phone, so it must be made by Apple, right?" Businesses don't want their credibility tarnished by interlopers who might reasonably be mistaken for the real brand by the buying public.
Copyright is afforded to a work as soon as it is created (meaning as soon as you write it down on paper or save it to your hard drive, for example, it is covered), and it is a negative right; it's purpose is to allow creators to decide who may use their works. As an aside, Creative Commons licensing functions because of copyright. The owner of a work can elect to allow any and all comers to use their material under a CC license, but only because they have the power to exclude use.
Generally speaking if you create a work that leverages trademarked names and incorporates copyright protected material (such as character names and plot elements from a published work), you're going to have to get permission from the trademark and copyright owners. Sometimes that's the same party, and sometimes it isn't.
Some heavy hitters turn the other cheek to certain forms of fan-created materials because they realize it helps maintain interest in their primary properties. For example, Paramount for a long time didn't hassle Star Trek fan film developers. I don't know if this is still true. Generally speaking, if fan fiction has a neutral or positive effect on the revenue-generating capability of the trademarked property, many rights owners will not hassle fans who create their own stuff.
It gets a bit trickier when they perceive that a fan-created work might impinge on their ability to make money off their property. For example, if you made your own free Heroes of Might and Magic video game, the rights owners would almost certainly come at you fast and hard, even if you weren't making money from it. First, trademark law actually mandates that they do so, in order to ensure that consumers aren't confused as to who puts out Heroes of Might and Magic materials. Second, your offering is now potentially an alternative to their own, meaning that some would-be purchasers could decide to just download your game instead of buying the official one.
The fact that you're thinking of making a tabletop RPG based on a video game franchise is likely immaterial from a legal standpoint. They certainly have the right to come after you. As a practical matter, a legal team will usually first send you a polite (or not so polite) note asking you to cease making your publication available. If you decline to do so and they feel you are diluting their brand or impeding their ability to make money from their works, they will come after you.
As @mxyzplk noted, the Steve Jackson Games policy is pretty reasonable and straightforward. That said, I'd send them a note telling them what you intend to do, in order to get them to bless their end of it.
I'd also contact the publishers for both the Warlord Battlecry and Heroes of Might and Magic franchises. Don't just send a note to the legal department. Try to find someone who is involved in game production - the higher up the food chain, the better. In most organizations the job of the legal department (or of the legal counsel on retainer) is to aggressively minimize risk. Anything new looks like risk to many attorneys, because they are trained to evaluate situations that way. So if you can get someone to bring the matter to the legal folks as your champion, after you've had a chance to lay out your idea to someone who will understand your intent and realize that it's a good thing, you're much more likely to get approval from them.
There are many reasons why fan-created works fly under the radar and are not pursued by owners of licensed properties. Most of it is simple cost-benefit analysis. The cost of hunting down fans, the negative publicity it elicits, and the fact that fans aren't even making revenue off it makes the benefit of keeping full control not worth the price.
I went into all this detail because I think that while the rights holders might never go after you if you created supplements using GURPS mechanics, this is also an opportunity to talk with the right people at these companies and help them understand that you want to do something that could benefit them. They may have fan contribution policies that don't easily accommodate something like the projects you had in mind, or they may have policies that do. Regardless, it seems that you'd have to put a fair amount of work into these projects. Knowing that you have buy-in from the rights holders would give you peace of mind, I'd think.