It’s written off as a business expense. Part of the house is used for business (so write off mortgage, home improvement costs), part of the employee time is used for home improvement (so labor is free for your own home).

You cannot say this with ANY degree of certainty. You don't know what he's attempting to write off. And it's Canada.... what is he even allowed to write off. But he certainly cannot write off 100% of the equipment he's buying, as it's going to live long lives outside of the video as non-company assets in his home for personal use. I cannot write off 100% of my cell service unless I show that it was ONLY used for business purposes.

I'm not sure I agree with your premise anyway. It's up to the ownership what to do with the money that the company makes. It's not the employee's decision at all... period. In this case those decisions were made by the CEO who happens to be the owner. CFO's garner their power for handling the money through delegation from the owner(s).

But in this case... it's actually true.

Can an employee get his colleagues to improve their own home at the expense of the company?

Yes... They can choose to participate in the $5k upgrades that LMG does. At this point I doubt Linus has any real direct interaction with the planning of these videos and just shows up at the personality on screen for shoot time.