Are there any virus risks for the online game Runescape by Jagex?

No. However, there are other sites that are disguised to look like the RuneScape website. They can try to infect you.

Usually you get links, just make sure if it Says "Click Here" or something like that to do with runescape, make sure you look at the bottom right of the screen - it will show where the link reads, if it don't lead to runescape.com (without spelling mistakes) then it's an attack site. in other words be on the lookout for spelling mistakes in the link.

Java may have an effect as well.