Is it acceptable to point out job offers in my graduate school application?
It's acceptable, but it probably won't help and could even easily hurt your application. It might be taken as a threat to the department, i.e. it's like saying, "I could take this fabulous industry job I've been offered if you don't admit me!" I might find this off-putting if I read it in an application. Departments aren't usually short of applicants, so a reviewer might just put your application aside thinking, "OK, you just go ahead and take that position. I have 50 more applications in this pile over here to go through."

Determination to do research isn't the most important factor in demonstrating your ability to complete a Master's or PhD program. The internship by itself helps show your passion for research, and maybe helps show that you're capable of it, but the idea that you're highlighting your willingness to bail on the internship in order to pursue a higher degree might say to some committee members that you're also willing to bail on the graduate degree program if something better comes along (like a nice offer from Google or Microsoft in you're in Computer Science). 

I think you're better off using the current internship to show that you are able to make progress in research, and leave the idea that you've been offered a job extending that research aside, lest you come off as pretentious or threatening. There are lots of suitable graduate school candidates with internships or prior research experience who might also be suitable to the same program. Use yours to show that there's something different about you.