The ability to 'Like' a post without logging in is very attractive in terms of surface level UX - The user doesn't have to bother with usernames and password, they just express an immediate emotion.
In order to retain a meaningful 'Like' system, the 'Likes' would need to be restricted to one per user per post. Without a login, the technical overheads become so expensive that it's not worth doing. You would need to write cookies, check cookies, and check IPs, and that still doesn't prevent someone using proxies or different machines to hit that 'Like'.
To retain an 'Like' system without a login and no technical overhead would render the 'Likes' meaningless as anyone could simply keep hitting like as many times as they wanted.
In both cases it may even be possible to write bots capable of 'Liking' posts on an industrial scale.
The only way to retain a meaningful 'Like' system is to make each 'Like' accountable - attributable to a measurable number of user accounts.
Of course this doesn't prevent cheating but it does make the effort/reward ratio much less attractive.
One route you could take is a persistent login state whereby the user only has to enter their details again if they have specifically logged out or not visited the blog for an extended period - this would allow users to express their emotion with the least amount of friction but would also maintain the meaningfulness of the 'Likes' they apply
The reason large social media platforms have you create an account is because they want to keep track of what you like so they can present you with more accurate advertising.
A more practical approach is that it is easier to for users to keep track of what they like when users have an account. As you said, a computer can have multiple users. What if all were 'logged in as a guest' and started liking different blogs and pages? You wouldn't know how to separate your likes from the others.
I do not know about your blog or product and what your goals are. I can imagine that as an owner of a personal blog you might not need user information. Likes and comments are all that matters. Think of this for your blog and make a decision based on this. Good luck!