Your sony tv has a 16:9 widescreen enhanced mode which was also known as "vertical compression". When you watch a widescreen DVD the tv has the ability to stop scanning lines where the upper and low black bars would be and compress scanning lines down to just the picture area which gives a much sharper picture and makes the scan lines smaller and harder to see. It was a cool feature that came out just as CRT TVs were on the way out.
Secondly, you not should to use the RCA jacks and connectors to the TV with your video player. Use the Svideo, rgb, or hdmi jacks depending on what was available when the DVD player and tv were manufactured.
Lastly, there seems to be some confusion on lines of resolution and scanning lines.
nTSC was/ is a 525 horizontal line system every 1/30 of a second. There is 262.5 odd lines(frame)every 1/60 th of a second then 262.5 even horizontal lines( frame)the next 1/60 th. these two frames make up a 525 horizontal line (field )every 1/30 of a second.this is called interlacing or the small "i" you may have seen before.
Progressive means all the lines appear at the same time. Ex. 480p, 720p, 1080p(blu ray)
Once all the flagging is done, etc. those 525 lines become about 480.
These horizontal lines are the vertical resolution.
VHS had 240 lines of horizontal resolution. That's horizontal. Vertical lines across the screen
dVD has about 500 lines or so lines of horizontal resolution.
All DVDs are authored with 480i lines of vertical resolution 480p happens inside the player, it is not on the disc.
Sounds to me that your DVD player is sending out a 480i signal to your tv, which is compressing those lines vertically and making them smaller.
I don't know anything about video games but it sounds like an older system.
But definitely replace the RCA connectors with something that can pass more bandwidth and at the very least your DVDs will look even better.