@Zing Thank you, I did everything, plugged RPI to different monitor and I had picture, then I plugged original arcade game which came with the cabinet and still had grey screen but sound was coming from the game. I found some horror stories of people damaging their screen with wrong PCB HDMI converter, which was sending wrong signal, resetting their display, etc. then I noticed I also bought wrong one, that's why bottom of the ES menu was cutting off in the first place! So while I was looking for replacement monitor on eBay I ordered correct converter suitable for my Arcade1Up display. I connected today and...
It worked! Display is sharp as supposed to be, all in great 4:3 ratio!
I literally went down on my knees and kissed my cabinet, hahaha!
Glad I didn't tell my wife (since she paid for my arcade cabinet) but I promised to myself to be careful and read everything twice before making a decision - and stop tinkering with Arcades and just enjoy playing it!
Thank you again for listening and replying 🙂 🙂