Demonstrations on the Wolfram Demonstrations Project are displayed as CDF files. CDF files are essentially Mathematica notebooks without input functionality, and on the Demonstrations project they're just single Manipulate output cells. If you want to make a CDF, you just need Mathematica.
The webMathematica demos are very dated, likely created well before CDF was even in development. All three interactive demos can be easily recreated with Manipulate and CDF. If you want to make a webpage, you can try embedding a CDF in HTML, or using the Wolfram Programming Cloud.
It should be noted that webMathematica is essentially a legacy product, as Wolfram has refocused its web efforts on new technology like the Programming Cloud.