Something that's going to be a bit tricky here is that electrons are really, really slow when we're talking about electricity through a wire. The electrons will bounce around very quickly at random, but the average flow caused by a current is slow. Really, really slow.
https://en.wikipedia.org/wiki/Drift_velocity
For a specific but not unreasonable example:
> Therefore in this wire the electrons are flowing at the rate of −0.000023 m/s. At 60 Hz alternating current, this means that within half a cycle the electrons drift less than 0.2 μm. In other words, electrons flowing across the contact point in a switch will never actually leave the switch.
That kind of speed means that any messages sent over a copper wire are not going to be sending electrons all the way for that message. The electrons that 'carry' the message "I AM A VIRTUAL SWORD" will not go from my machine to yours as a rushing block. Instead all I'll be doing is tapping the end of a very long pole connecting our two properties, so you can read the message by the patterns of the end of the pole in your house moving ever-so-slightly.
So, I guess I am transferring mass, but nothing that comes from me goes to you.
This also assumes a very particular direction. There's nothing, as far as I'd understand, that requires me to be pushing electrons at you. I could be pulling on the pole slightly rather than pushing.
I'd love any corrections or additions to this, purely my lay understanding of the topic.
Also with waves in water; put a ball floating at the beach and it'll mostly stay put bobbing up and down. (It's only when the waves actually break that there is substantial movement of actual "bits" of water.)
It seems to me that the question of whether or not electricity has mass is a proxy for whether or not information is tangible. This is the same interpretation that "Greg Graviton" at stackexchange has. And it is hard to meaningfully answer by yes or no; information needs material in order to exist, but by itself it is not tangible. Both yes and no are misleading.
My advice, which is completely ignorant of how law is practiced, is to find another way to settle the original question of whether or not the coerced obtaining of the virtual sword could be named "stealing". When taking intuitive notions such as "is this a _thing_ or not?" to the fundamental levels, the questions often stop making sense, as it has in this case, because the intuition is dependent on another level of abstraction. At this point it is no longer constructive to attempt obtaining answers to the questions as posed, and maybe this is why you have struggled to find a good answer. That's probably not helpful to you, but it is my best attempt at resolving this question :)
(About DC: It is more accurate to say that there is an exchange of mass. The same count of electrons go down the wire as up the other wire. There is no net transfer of mass. See also https://news.ycombinator.com/item?id=14087221 )
Thanks for your contribution; as I mentioned below, I've gotten some different answers, e.g. on http://physics.stackexchange.com/questions/2188/does-electri... where I asked the first time. Essentially, are you saying that with DC current, there is transfer of 'mass', but with AC, there isn't? In the case such as I've explained it elsewhere in this thread, this might mean that it matters how a computer is build to decide on whether the virtual sword can be stolen or not... (maybe, I haven't really looked hard at it in a few years, so I'm probably forgetting some details of it).