This is a good question. I really don't know the answer. I imagine it has something to do with electrons being treated as a gas for some specific application. I really have no idea, though.
Why would you write that? In what context? If you are talking about a reaction that happens thermally, at extremely high temperature, such as in the upper atmosphere of the Sun, then you are talking about an ionization reaction. At temperatures well above 10,000K electrons can be removed from atoms, producing a "soup" of ions and electrons called a plasma. It's not completely unreasonable to say the electron is now in the gas phase, but it's also a little misleading, as the properties of a plasma are nothing like those of a gas -- it certainly does not obey the ideal gas law, for example -- because of the very strong long-range electrostatic forces between the ions and electrons. On the other hand, if you are writing an oxidation half-reaction, those are theoretical constructs -- they do not describe actual events, but rather imaginary "halves" of a complete reaction (a redox reaction) that actually does occur. Most redox reactions you study will happen in solution, but there's no reason why you can't contemplate them in the gas phase. But in either case, there is not a lot of sense in putting a physical state symbol on the electron -- because it never actually exists as a free entity. It goes directly from one bonding situation to another, without floating around in the gas phase or solution for some measureable amount of time. In either context, I would say it isn't very accurate to put a "(g)" after the electron, and I would certainly not teach students to do that. However, some instructors do want their students to essentially robotically add physical state symbols after EVERY reactant in EVERY chemical equation they write, and if your instructor is one of these, then (g) is about the best you can do if the reaction under consideration happens in the gas phase.