[Q] Issue with Chrome and HTML5 vs Flash videos topic

Model: LG G-Pad 7.0 v410 ( AT&T)
Firmware: CM 12.1 Nightly - Lollipop 5.1.1

Hey guys,
I read the post about asking questions, so I'm going to try to make this organized and all inclusive. I apologize in advance if it's too long.

Preface: I'm a long time iOS user. I got this tablet for free with some AT&T promotion and I'm glad I did. I'm loving Android and how customizable it is.

Background: Chrome for iOS can only cast videos to Chromecast if the website has enabled the functionality. But I read a few articles (Engadget, Lifehacker) that described how Chrome for Android can cast any embedded video to Chromecast as long as it's compatible (HTML5 MP4). This was great news because I could really use this with my current situation. I'm a medical student, and I'll be taking the Boards in 2 months. I have bought a few 3rd party resources for prep. They provide various materials, including video lectures (and there are a ton of them).

Problem: When playing these videos on desktop browsers, they play as Flash videos. But when they are accessed on a Mobile browser, they play as HTML5. This works fine on my iPad when using Safari or Chrome. But I wanted to cast them to the big screen. So I navigated to the videos in Chrome on my Android Tablet. But, instead of falling back to HTML5 video, the player frame displays the message "Flash Version 10.1 or greater is required. You have no flash plugin installed. Download latest plugin here." This situation is true for 3 of the 4 different sites I'm using.

Things I've Tried: I uninstalled Flash a few days back. But thinking maybe it had something to do with the fact that it was ever installed at all, I wiped cache and rebooted. But I still got the same message. I searched and searched and searched some more (Google). But the hits I kept getting mostly had to do with with Devs on forums trying to fix their own site or how Flash died lol.

THE Question: Is there anything I can do to fix this (or any workaround), or is this something the developer of the website has to change on their side? (If that's true, then wow I wasted a lot of time lol)

Questions just for my understanding, nothing really necessary:
-What is the difference between iOS and Android that's causing this inconsistency?
(I mean obviously they're different, but I figured websites identify them as "Mobile
Devices either way)
-Why do these websites see Chrome on Android as a browser that supports Flash?
-I know I can just mirror from my computer, but Casting would just be easier in my
situation as it is. I also just really want to understand this problem.

On another thread, the developer of vGet describes the weird website situation nicely.
"Mobile Mode: Pretends to be a Mobile browser without Flash support. Some sites support HTML5 videos, but only use them if Flash is NOT supported by the browser (which is kind of silly but it happens)."

Here is a thread I found of someone with the same issue. (But it's kind of old, and the solution was to use a different browser and install flash, which doesn't work for casting).
http://forum.xda-developers.com/show....php?t=1815642


Thank you in advance for any help you can provide. I reall do appreciate it. And I'm sorry again if I went into too much detail.