Imo, if I was reading a CV, ideally first I'd want to see stuff on the CV that looked vaguely alright, then a webpage with a list of links to your work, screenshots, videos (e.g. youtube) and download links. Then some code examples, some working projects on github or something, so we could see your coding, be selective and try and show your best work.
As for web builds, yeah sure do one if it does justice to your demo, if not just have the full build link and videos. They will download if interested. Don't email it, no one wants an inbox full of 1000 demos.
I'm not clear on what type of game jobs you are applying for, I'm assuming using unity and c#? There is a distinction here between applying for a job using high level language and a pre-existing engine, and actually writing low level stuff, usually in c++. What language have you been using for your non-game job for 9 years?
Some completed mini-games would be good to show all round ability in any case, but in the case of low level programming especially, you will often be applying for a specialized area (e.g. graphics, AI, sound, tools, networking, animation, physics etc etc), rather than jack of all trades. So in that case you would need to decide on what you want to work on, get good at it, and do some demos of this to show it off.
If you are showing something that is from a previous employer, make sure you have permission, and explicitly say 'by kind permission of blah'. Also make it explicitly clear exactly what you have contributed to anything you mention, don't try and claim credit for other people's work.
Personally although I'd never entertain someone pitching a 'great game idea' (for the legal reasons mentioned earlier as well as many more), I would expect to look at games / demos created by a job applicant. This might vary depending on company policy though.