Yes, I think the portrayal of LDS doctrine in that video is pretty much how most non-Mormons would explain it. It's a far cry, though, from how we would explain it. In this case, fiction is truly stranger than the truth.
I'd say that's a very simplistic and, consequently, not a particularly accurate way of putting it. But, there is a small element of truth in it as well. Allow me to explain...
We believe, as the Bible states, that we are the offspring of God and that He is the Father of our spirits. We believe that we are more than just His "creations"; rather, we were created in His image, after His likeness. With respect to becoming gods of our own world, what we actually believe is a doctrine called "Eternal Progression." The same general idea (Deification, i.e. "Eternal Progression" in LDS parlance) was clearly taught in the early days of Christianity -- not by random heretical sects, but by noted Church fathers:
Irenaeus:
“If the Word became a man, it was so men may become gods. Do we cast blame on Him (God) because we were not made gods from the beginning, but were at first created merely as men, and then later as gods?”
Clement:
“The Word of God became a man so that you might learn from a man how to become a god.”
Saint Justin:
"[Men are] deemed worthy of becoming gods and of having power to become sons of the highest.”
Athanasius:
“The Word was made flesh in order that we might be enabled to be made gods. He became man that we might be made divine.”
Augustine:
“But He that justifies also deifies, for by justifying he makes sons of God. For he has given them power to become the sons of God. If then we have been made sons of God, we have also been made gods.”
In much more recent years, the noted Christian scholar, C.S. Lewis, said,
“The command Be ye perfect is not idealistic gas. Nor is it a command to do the impossible. He is going to make us into creatures that can obey that command. He said (in the Bible) that we were 'gods' and He is going to make good His words. If we let Him – for we can prevent Him, if we choose – He will make the feeblest and filthiest of us into a god or goddess, dazzling, radiant, immortal creature, pulsating all through with such energy and joy and wisdom and love as we cannot now imagine, a bright stainless mirror which reflects back to God perfectly (though, of course, on a smaller scale) His own boundless power and delight and goodness. The process will be long and in parts very painful; but that is what we are in for. Nothing less. He meant what He said." (Underlining is mine.)
Here is an article from the official LDS website called
Becoming Like God. It's fairly comprehensive, but long too awfully long and very understandable. (Incidentally, you have to click on "Read more" at the end of the second paragraph on the page.) I hope people will take the time to check it out. At any rate, we do not believe that "upon death [we Mormons] can become god of [our] own world." On the other hand, we do believe that with God, all things are possible and that if it is His will that His children eventually become like Him, it will most certainly happen.
Actually, we don't believe there is any ritual in the world that can "make a person Mormon" and no one other than Jesus Christ can "save the soul" of someone else.
Here's an analogy I've used to explain the practice of posthumous proxy baptism in the past:
Let's say I was crazy about Carrie Underwood (which is not the case, incidentally) and you really didn't care for country music at all. I knew that she was coming to town to do a concert. When I bought my ticket, I bought an extra one for you (without you asking me to). I then mailed it to you and told you that I really thought you might want to reconsider and go to the concert. I was sure you'd end up liking it and I didn't want you to miss the opportunity. After all, I'd already bought the ticket. At any rate, you
would have a choice. You could either decide to use the ticket and go to the concert or toss it in the garbage, thinking, "Katzpur knows I don't like country music. She just wasted a lot of money on something she should know I wouldn't want."
That's how we see proxy baptism. It's an ordinance (i.e. sacrament) we perform for someone who has died, believing that if a person can change religions during his mortal life, he can do the same during the period of time between his death and his resurrection. The baptism itself accomplishes nothing on its own -- just as my purchase of an expensive concert ticket and the time it took me to mail it accomplished nothing if you chose not to use it. If the deceased person accepts the baptism, a true conversion has taken place. If he doesn't, it's just like your throwing the concert ticket in the trash.
We don't have any way of knowing who accepts these proxy baptisms and who doesn't, and we do not increase our membership numbers by the proxy baptisms we do. I realize that's just a nutshell explanation of the doctrine, but I don't want to bore you with any more than that unless you want to delve deeper into the doctrine.