I learnt this the hard way when I was kid because I carried felt tips once on a flight (for drawing) and had them leak. They were the thinner type of felt tips used for colouring though, so not sure whether this affects the thicker kind of permanent marker yours seems to be - but I assume some other products may be affected the same way due to cabin pressure. Since luggage compartments on aircraft aren't pressurised at sea level either, I'm assuming the same would be true regardless of whether you take it in cabin or in checked luggage.
(I was also carrying fountain pens on that flight. Yes, it was nasty.)