Well, the title is auto explainable.
I can play html games that are only one archive, but I can’t manage those games that has an (for example) index.html and a folder with audio, pictures and other files.
I advice that I play mostly on Android and ios systems.
It is possible that some of the IFComp entries may have a download option that works for Android, although there are no guarantees. If a HTML-based game does have a download option, then you would use it. Make sure it downloads to its own folder to prevent overwriting issues or guesswork about which file is associated with what program (HTML-based games can have thousands of files).
Afterwards, you can play the game via its index.htm file, using your phone browser. (Some of the Twine games are designed so this is possible, some - for various reasons - are not). Depending on security settings for your phone, you may have to download onto a desktop/laptop computer and then transfer the file, but by default I would expect iOS and Android phones alike.to be able to do this.
There is at least one IFComp HTML entry (The Corsham Witch Trial) that allows the main part of the game to be downloaded, but requires internet access to Google Drive in order to see certain clues. You may be able to work around this by going there while you have online capacity and then downloading the clues for later offline play, depending on their format.
If a HTML game in IFComp does not have a download button, then unfortunately it is probably not designed to permit offline play. (Generally, trying to manually download HTML-based games without going to a place where the hard work’s been done for you by the author does not tend to go well).