I want to publish my game for free.

I want to publish my game for free. Can I do it for free?

If your game is free and you not earning money out of it or indirectly (crowdfounding, ads in it etc.) then yes, on service that let you publish free ofcorse

Read EULA everything you need to know is there:

There are online venues where you can distribute and publish your game at not only $0 for the customers, but also costs YOU $0 (no fees, no royalties, etc. taken by the store/venue).

I’m not sure but I think is one such place. They charge very little and maybe nothing for a storefront and download hosting for your game files.

One the other hand, it is industry standard for an online platform to take 20-30% of your profits before you are charged taxes by the government, so you end up keeping only around 40-50% of the proceeds from sales.
Steam is like that, plus they charge $100 for each game you post to your store. But you will probably get more visibility out of the box there than elsewhere. So with Steam then you’re losing at least $100 even if you don’t make any money off the game that they might withhold from your sales if you did sell for more than $0.

But really you can host the game files in a ZIP anywhere you want, even off your cloud drive like OneDrive, Google Drive, or DropBox, if you want. It’s not a storefront/venue so there’s no way people would stumble across it, but you can do that way too.