You'll have to use a different browser other then chrome to download the RSCE client since it blocks java. Try Firefox.

But even then, the chromebook itself wont run it due to it not being a windows operating system, and i cant use an apk. because i dont have anything to run the apk on the chromebook.

step 1. make sure your chromebook is x86_64 using COG
step 2. visit https://www.java.com/en/download/linux_manual.jsp and get linux x64 from the page
step 3. open your chromebook settings and turn on your linux beta (x86_64 only)
step 4. in your file browser, drag the download from earlier into your linux files
step 5. open your linux terminal from your app drawer
step 6. type in sudo su for root perms.
step 7. type in tar zxvf jre-8u261-linux-x64.tar.gz
step 8. type in cd jre1.8.0_261/bin
step 8.5. make sure you go back to being a regular user su USERNAME
step 9. make sure the game files are in your root linux files and run ./java -jar /home/USERNAME/RSCE_Launcher.jar from the jre folder