That is correct - if you are trying to get to US via H1B (though, there are other types of Visa - of course - H1B being most popular), then there's little the company can do about the annual limits. You'd have to wait and file the petition when the slots open up (for a day or two each year) - which is something that game companies do not really have to do, since there's an overflow of applicants into the gamedev grinder anyway.
I should have been a bit more specific. It's much easier to get transferred to US as a SW engineer outside of game industry.
After all, why should the company even bother with the whole Visa process, if there's an overabundance of local candidates willing to work for peanuts (or less) ?
Now, if they identified the exact match for some senior candidate, and they have a process in place to handle the paperwork AND they know they can wait 3-5 months till the interviews at US embassy take place, passports get stamped (and so on, and so forth) - Yes - it can happen.
But, I don't really think it's a very probably scenario, since here in US, there's a gamedev layoff every few weeks anyway - so there's lots of senior candidates ready to start working right away. Plus, the job mobility is an order of magnitude higher here (than in most parts of Europe). If you get through the phone IW on Monday and they tell you to come for onsite IW on Tuesday, you just jump on the plane and go...