I got a pretty sever concussion 2 years ago and since then I've been living with my by then recently widowed grandmother of 80 years old who's kind of an alcoholic with kind of a poor diet.

Ever since my starting living with her, her alcoholism has been under control and she drinks "only" about 600-700ml of wine a day, in three doses. Reducing it further seems unrealistic.

Anyway she used to have quite a lot of pretty strong neurotic fits over nothing and seemed to be very anxious about things. Having read up on various food supplements because of my concussion, I figured she might be deficient in magnesium and that trying to give her some wouldn't hurt.

I didn't expect much from it (I'm a fairly skeptical person, especially after learning that pretty much no supplement helped me with my concussion), but the effects of the magneisium lactate pills I bought her (0.5g or Mg lactate per pill (51mg of Mg), I've been giving her 3 and later 2 per day) seemed almost magical.
Her mood became a lot better and stabler, and she started thinking much more clearly very soon (~1-2 days) after starting taking it.

Anyway, I've been giving her those pills for several months now (about two times, she decided she'd stop taking them, and her fits came back so I told her no wine unless along with an Mg pill). The label really says it should only be used prophylactically for 10 days and longer use should be consulted with a doctor.

Do you think it is safe to keep giving her those pills?

The elderly usually have poor kidney functions. Therefore they and also infants are the typical statistics for magnesium poisoning, since they cannot clear it from their body's excesses.

Usually this happens with magnesium based laxatives and enemas, but it can happen with oral supplements too.

I'd ask a doctor, and have her tested for kidney clearance before continuing with long term supplements of magnesium, as this can build up in the blood, if the kidneys are not filtering well.