My girlfriend left me for missing my date night

Hi, I don’t want to reveal my name as I might get bashed for being a ‘man-child’. Let’s just assume my name’s John and my girlfriend’s name is Ashley. So this is something that happened on the day of second date anniversary and I somewhere regret it but my girlfriend is making a big deal out of it. 
To begin with, I wanted to surprise my girlfriend and make it really special with a candlelight dinner setup and some roses as she likes it. And it’s not easy for me to plan any surprises as my work schedule is very hectic and I cannot afford to take off any day to get this ready. Since it wasn’t possible for me to arrange this, I asked my sibling to help me arrange this on the terrace. I also got my girlfriend a beautiful dress for the date it makes her feel special. 
I have been addicted to mobile games for a while now and that happened because my girlfriend keeps playing them on her phone to help with her anxiety. Watching her play all day made me play the games and whenever I feel the work pressure, I just play. Coming back to the point, that day was one hectic day and my boss kept pressurizing me for completing my tasks as well as the tasks that my absent-minded colleague had. I couldn’t deal with so many things, so taking a short break, I started playing games and I obviously kept playing for so long that it was very late in the evening. I came back and started working again without knowing the time. By the time, I finished it, it was midnight and I completely forgot that it was our special date night and I had kept my girlfriend waiting. 
First thing, I went straight to my girlfriend’s house to apologise and make it up to her. She did not listen and closed the door in my face. The next day, when I called, she asked to break up for missing my date night. I asked her to understand my situation instead of blaming it on me. At this point, I feel like what’s the point of staying together for 2 years and not understanding such situations? It's not like I missed the date on purpose. She feels like I am cheating on her while giving such excuses. I sincerely regret that I could have planned the date for some other instead of keeping it on a busy day, but she isn’t ready to accept my apology. Am I being a bad boyfriend for this? Hope to hear some suggestions or advice on how to fix this issue with my girl.