MyBB Community Forums

so i've read this tut community.mybb.com/thread-27771.html
but noticed it's 3 years old so i just wanted to make sure.

Could i just simply download all forum files agin from mybb site, upload via ftp and use backup i downloaded from old forum?
Thanks.

Yes, that thread is still valid ..
remember to keep copies of earlier config.php & settings.php files AND modify them as required

but can i just simply install a new one on new host and just use backup to recover users and posts?

You could, but you'd lose all themes and plugins.