don't know the difference between them and computer engineers, feel free to help me out here
Software engineering is one of the fundamental aspects of computer engineering, and precisely is the one that deals, for instance, with organization of the software production process from the specification to the deployment.
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Software Engineers (don't know the difference between them and computer engineers, feel free to help me out here) and game developers, especially if they're alone or in a small team, work differently, on different kinds of things, so i don't think it's that easy to compare them on the spot.
Professional game developers are in fact software developers, and their work is subject to all the aspects of every software development process, among which lies the paramount duty to respect deadlines. To understand the importance of this, let me tell you a real-life example:
A game must be developed, and the company employs three guys to work on some physics simulations, and gives them a three months deadline (not sure about the number, maybe it was four months, but it's not important for our story); now, two of them complete their work respecting the deadline, while the other one is horribly late and asks for three more months to complete its job. Do you think the company would never agree to that, thus having to pay more in terms of development costs and wages (many developers are hired with project contracts) and risking to hit the market too late (remember that markets such as the game market evolve very rapidly, and what's interesting a day may become garbage after a couple of weeks)? To be clear, the company obviously did not agree and fired the slacker (and had the two other guys work on his part, which they completed in about one and a half months, but it's not interesting for us right now).
That, sir, is how serious and professional software development work is done. And when you receive money from other people, be them your employers or your patrons, you
must be serious and professional.
That is my argument as a professional. Now, please let me discuss a sentence you wrote:
"he missed a rough estimate he was giving out months prior" is NOT anything of the sort.
The sentence you quote is actually a perfect argument, if you ask me: each and every professional software project (and, as stated above, when money is involved the thing is obviously professional)
must begin with specification and planning phases in which times are discussed and decided that must be absolutely respected.
To be more precise, many games are developed using processes similar to the infamous Agile methods, which almost always require to define major development steps at the beginning of which the work to be done is divided in minor steps associated with deadlines which must be respected.
So, please, don't go around telling that missing a deadline is not a problem: when you develop software
and are paid to do it, missing a deadline is one of the most serious problems.