Yea, I'm watching the UPS thing. If that takes hold, then don't expect to get much delivery of anything. Doesn't matter if your end product isn't shipped by UPS; it's so big, it will cause ripple effects on all other delivery services and stores.
As for LRG, I wonder what their overall thru put is for deliveries. Assuming they're not slave driving, six picks an hour (that's print labels, get games, get boxes, double check, pack, affirm, and ready for post), 8 hours a day, 5 days a well, 4 weeks; that's 960 shipped per worker. Eight workers is 7680 a month. It would take 4.5 months to dig out of a backlog of 35,000 titles.
Now I have no idea their average picking rate and order complexity. Single order standard releases go out fast and likely have a dedicated team. Complicated releases are likely much slower than six an hour since you have to triple check all the products, their condition, and pack with greater care (in theory).
All while assuming all standard shelf product (panstock in my world), such as boxes, tape, printer labels, etc. never run short and the distribution system has a 100% up time with a 0% error rate.
Many variables can also limit thru put, meaning it may not be so easy to throw bodies at it, such as the physical layout of the shipping area(s), how product is binned, how incomplete/pending orders are stored, and consistency of staff (ex. training status, turnover, etc.).
I just made up numbers, but a small operation like this churning through 35,000 unique deliveries is a big chunk, more so with only one distribution center.