Your reaction reminds me of a family member of mine. She used to play a LOT of cash poker. When we first started playing together she would whup my butt. EVERY. SINGLE. TIME... But lately I have been playing a lot more than she has, and I'm finally getting a read on her. The last two weekends we played some games together and I took her for all she had. I could see that same look in her eyes that you describe feeling. I honestly felt bad for her, she seemed so drained of life over the losses. She takes poker very seriously, and me not so much. But I know good and well that she is going to come back and put some more beatings on me at some point. Just as you will to your opponents too.
Without getting too into the details and airing out dirty laundry, poker definitely is the reason I'm still here today, so it has a weird relationship with me in my life currently.
It's the only thing that actually pulled me out of a really dark place in my life. I started taking care of my health again (which is why I just had my surgery), started reading again, applied to college so I can use my GI Bill, stopped smoking cigarettes, stopped my spiral of alcoholism on its own (I was drinking 6 days a week minimum), and has brought back my confidence and really has breathed life into me again to be honest.
Since poker is a game about life too, and what it has been doing so far for me, it is more than just a game that I enjoy immensely. I tend to take it seriously and is almost as a reflection of how I am doing personally. I kinda owe it to myself and the game to research it and learn as much as possible at this point. I get excited when I get a new book now, where as before I hated reading and had (and still kinda do) have issues reading and retaining info from my head injuries. Since I started playing, my ability to retain information has been increasing, my situational awareness has improved significantly, I'm starting to become a little more introspective and honest with myself, and I have been a lot more motivated to get up and "get out of bed" as you will.
So when I make mistakes, I beat myself up a little and try to figure out where my leaks are, because it wont only just fix my poker game, it bleeds into my personal life too. Everyone in poker and life takes bad beats, and learning how to deal with them in poker is helping me do it in real life and vice versa. When I start to make mistakes, generally it is either out of ignorance from my inexperience, or something in my life is bothering me more than I thought before and it compounds the frustration that normally isnt that big of a deal. When I realize that my reaction to stress or whatever happened is unreasonable (more than just a little frustration that leaves soon after a bad beat or whatever) then I can isolate the issue thats making me react that way and deal with it. Then the leak gets fixed when I identify the issue, deal with it, and I start to do a little better again.
So I guess I get a little too invested in it based on the role the game plays in my life at the moment. As I get better at poker and fix the real life leaks I have, the game will become more and more of a hobby for me and I will be able to relax a little more as time goes on. As it stands now, poker saved my life and I owe it to myself to keep pursuing improvement.