First, the question is a bit on the open-ended side. "...any idea of the simple ideas repeated each game to game in the old style retro games." It's too wide a discussion to pick any specific answer. If you had a more specific problem set, you might get better responses from others.
Specifically to your case, as mentioned in the comments you should not be trying to copy Snowbros. class framework and code design in your project. (Snow Bros. wouldn't even have had "classes" anyway.) Libgdx is a perfectly fine framework to recreate a Snowbros. clone. For each task you want to get done, think of how you want to do it for the platform you're currently working on, and implement it that way.
Now, that's not to say you shouldn't try to emulate "retro" effects in your new platform. For example many old games have slowdown when many objects are on the screen. Depending on your code and your Android platform, this will likely never happen with your simple game, but you may want to recreate the effect in same manner, most likely artificially. You should NOT, however, try and recreate this with bad code. It won't even come out the same way as a "retro" game anyway.
Besides all this, judging by the formatting of your question, you're getting way ahead of yourself. Just try and get your game done and working in the first place. Once you have basic things moving around, maybe then think about emulating a "perfect" retro feel. The most important thing first is to even get a project done.
It's good to think about the "right" way to do things, but especially for game development, at the end of the day/week/sprint you should just get something done. Don't let "right" prevent you from getting a finished product.
Lastly, deltaTime is a perfectly fine value to use for your update loops. Snowbros. probably would have had a constant framerate - if you want to copy this, set
deltaTime to your desired framerate before you make the
.update(deltaTime) calls in
deltaTime = 1.0f / 30.0f; // "30 frames per second" and don't care about slowdown
for example. Then maybe later you can implement some kind of fake slowdown later if you get that far.