Yufuin onsen for foreign visitors ?

After checking out the photos and info, I think I like to spend more time in Yufuin but it's mentioned here only one public bathhouse is open for foreigners and it happens to be the one with least facilities, only gender mixed bath and no proper changing room. How about the other first 3 onsens mentioned in this site ? Are they not for foreigners or onsens are not considered bathhouses ?

but it's mentioned here only one public bathhouse is open for foreigners and it happens to be the one with least facilities

No, you confuse "foreigners" with "tourists". This is what is mentioned:

the Shitanyu, can be used by tourists, while the others are for use by local residents only.

How about the other first 3 onsens mentioned in this site ?

They are baths by local ryokan which are open to non-staying guests during daytime.

Are they not for foreigners

No bath houses in Yufuin maintain any discriminatory rules based on nationality.

or onsens are not considered bathhouses ?

The first three baths are part of a ryokan, while Shitanyu is a public bath house.

Onsen = hot spring

Thank you Uji-san,

Actually I am slightly confused on "public baths" and "hot springs or onsens". As foreigners or tourists, we will think that the "hot springs" are also considered "public baths" since we can take bath in it.

My kids used to play in that Kinrinko lake straw hut onsen public baths.
Usually a publick bath is called "Sento" & uses heated tap water and provides stand alone service for locals who don't have bath in their house. The entrance fee is very cheap or honor system(rare) like the one you are looking at. Onsen public bath is unusual except for the onsen areas.
Onsen means just earth heated natural hot spring bath. Some so-called onsen in Tokyo, Kyoto area where the spring water is not hot enough may heat the water by boilers & still classified as onsen.
The real onsen that I use is called "Kakenagashi" onsen, once through, not recirculated or heated as abandoned amount of hot spring water is available like in Yufuin, Beppu, etc. and may need to cool down by tap water, if too hot (many are. You will see steam rising in the air). The wash area has the tap water.
Ryokans/hotels offer accomodations and meals in addition to onsen for tourists & not for daily locals use.
Standard onsen is gender separated and large. But if you need privacy and out door roten onsen bathing, I can recommend a ryokan I use often in Yufuin at a very reasonable rate.

Onsen simply means hot spring. Tourists can find onsen baths mainly in two types of locations:

1) public bath - an establishment that specializes in providing baths

2) lodging - a ryokan or hotel that maintains onsen baths. Some lodgings open their baths to non-staying guests during daytime at a fee