Videos
All I can find about, is deprecated stuff od 10 years ago
On the desktop interface it looks fine, but once you see the mobile version, you see All the content/photos one by one which makes the page extremely long
I think your negative impression is right. It doesn't implement the features you'd expect in responsive design.
The key to your question is that Google Sites don't use a viewport declaration (meta viewport in the head element). If you don't have that, then device browsers treat you as a legacy desktop-only website. They assume you'll break completely below ~830px, and set a page min-width accordingly. That doesn't sound much like responsive design to me.
Google Sites don't let you write your own CSS or HTML HEAD, so you can't implement a more responsive design yourself.
To be fair, you can choose to not set a fixed page width. Also navigations buttons will reflow on relatively narrow windows, if you're using the "horizontal navigation" feature. The latter isn't great design but at least it's degrading gracefully.
There is an option "Automatically adjust site to mobile phones" under Manage site -> General. However many people suggest it's better not to use it :). I tried enabling it on an old site, previewing the page, and selecting "preview in mobile". At least on Firefox on my original netbook (800px width), it was not responsive. It didn't expand to use the 800px screen properly.
As an aside, the line-wrapping (or absence of it) is a pre-existing issue with my site. You could blame this on me for not testing it :). However it illustrates a limitation of the WYSIWYG editor in Google Sites. It doesn't show, check for, or filter out the formatting that causes this problem.
Mobile yes, responsive no.
I was messing with Google Sites today and you can make a site mobile friendly (I had to come here to get started!). I just used the "Blank Template" to mess around with.
You do need to activate (like others that have mentioned):
Options (gear icon) > Manage site > (scroll down to Mobile) Check.. Automatically adjust for mobile phones. Yeah, let's bury that option way down at the bottom!
Considering the whole mobile "push" Google implemented in the spring of 2015 this should be ON by default for any newly created Google Site.
Just selecting that option makes an OK (basic) mobile site. Not a responsive site. So on my iPhone it does scale photos correctly to fit the device and switches the main horizontal menu to the "hamburger" icon/menu. But collapsing the desktop browser window does not produce responsive results. https://sites.google.com/site/rwstws51/
As a test, I uploaded a way too large photo (2.5mb) to see what would happen. Running the site through Google PageSpeed Insights it did not display any "optimize photos" warning, so seems to serves up an optimized photo for phones and desktops.
I guess the basic theme is actually called "Ski." I tried out the "Legal Pad" theme and it was totally borked on mobile. I think due to the header and content area background images.
To me Google Sites is ideal if you are already heavy into Google's other products... drive, docs, Google+, webmastertools, analytics, etc... As it has links to add those types of items when editing. Or need a quick site for collaborating as you can easily set the site access like YouTube,Drive items.
Also, you are very limited as to what html you can added. Trying to add a script tag gets stripped out when attempting to save. So again depending on the use there are definitely other options out there.