Unions work where labor is interchangeable. That is definitely not the case in game industry, where people are highly specialized and super creative.
For example, from https://www.wga.org/the-guild/about-us/guide-to-the-guild
"We are the Writers Guild of America West (WGAW), a labor union composed of the thousands of writers who write the content for television shows, movies, news programs, documentaries, animation, and Internet and mobile phones (new media) that keep audiences constantly entertained and informed. "
If you are a television producer hiring a writer, you don't go to the WGA. You just interview a bunch of writers, select the one you want, and offer them the job. Like you would any other job, really, except that if the writer is a member of the guild then the terms of employment must meet some certain standards, with rules about crediting and overtime, etc. But so long as you adhere to the guild's rules, it's like hiring any other independent contractor.
But if you're a ship captain wanting to offload cargo, you go to the longshoreman's union and as for N day workers. You don't pick who, and you don't negotiate rates other than specifying (and paying for) the desired experience level. You ask for N longshoremen, and you get N warm bodies and the bill.
To the point of this conversation, a guild makes more sense in a creative project where the skill and art of the worker matters to the end result. If you're producing a TV comedy, you really need to make sure you employ the correct writers. Likewise for game designers.
That being said, even if you don't accept that, there are unions (not guilds) for independent contractors in the creative fields for example in the UK the musicians' union and Equity (the actors' union). If you are hiring musicians or actors in the UK you will for sure be hiring the specific people you want and they will very likely be members of the union.
Your example about hiring union workers may be how it works in the US but is not the case in other countries - you would hire them just like any other independent contractor or employee.
Source: I have been a member of both creative and non-creative unions in my career. I've been in the musicians' union and my wife and many friends are members of the ISM (another union for musicians with more traction in the classical music world) and I have also been a member of a more conventional union (the GMB or "General Municipal and Boilermakers' union") believe it or not. In no case have I ever been hired on the basis of a process like you describe.
I take my 40h week, health insurance, vacations anywhere I feel like, paid overtime, over some magical wage in exchange for less benefits that exploit working class.
Anyone that feels it isn't their thing is free to make their own business, free of union agreements and see how they manage for themselves in the market.
In the United States this is not true. In many states once the union is established in an industry, it becomes illegal to operate a new business without the union.
We have bad union laws.
But also I didn't say union laws are bad. There are some specific industries/occupations in which unions are A Good Thing. What I said is that the laws we have around unions are really non-ideal and lead to worse outcomes for everybody.
I happen to see it in other way.
Then again, I surely wouldn't like to be on US during the McCarthy era.