HitMeNone,
It's good that you've been having sex with her. The fact that she's texting some other guy abroad all the time - not really something to worry about, but it may be an indication of something important. Keep reading and I'll explain why.
So what you're doing now is basically stating through your ctions that you two are closer than casual. If you see a girl once a week, you will be leaning towards commitment, and she may not even have the 'talk' with you if the two of you are seeing each other often enough. For girls, actions speak louder than words, so the fact that you're seeing her more than once a week is a clear indication that you're committed to her, as opposed to remaining casual.
If you aim for a casual relationship, you want to be seeing the girl once every 10 days on average. The fact that you see the girl less than once a week indicates that you two aren't that serious.
Now, let's discuss your situation. The fact that the girl is texting this guy everything, I wouldn't worry about it. Eventually they'll tire of each other. You're probably wondering, "Well damn, this is so annoying, what can I do to really up the attraction and get her interested in me?" Well I think the problem here is, you may not be taking care of what the girl needs bro. If you were, she probably would have no interest in the guy whatsoever. I feel like you're being a bit aloof with your feelings towards her, seeing her for sex then leaving all of a sudden. That's what a casual relationship is, but even in a casual relationship, you need to make your girl feel good. Hold her after sex, talk to her, deep dive, get her more connected to you. You are in the relationship so you can start becoming a bit more authentic with her by now, including being a bit more romantic. That by NO MEANS suggests you should drop all other girls in your life, stop meeting new girls, getting numbers, etc.
If you want this girl to really like you a lot, take care of her emotions more than you currently are. With that being said, don't start taking her out to dinners all the time, unless you KNOW you can manage that throughout your ENTIRE relationship. Set low expectations; high enough that she'll be happy, but don't take her on expensive trips, dinners, buy her things all the time, unless you want to keep doing that for the remainder of your relationship. If you do all of that then stop, she'll be attracted to the stuff you were doing for her/giving her, and not you as a person. Also, she'll get upset because 'you weren't the same guy as before', and she'll assume your interest has dropped as a result.
Conclusively, if you want to get committed, that's fine, so long as you don't cut all external options off (friends and girls) because that's stupid, poorly planned, impatient behavior. When people follow their emotions all the time, especially in relationships, they'll get that "high" for a while, then it'll come crashing down in a trough and you'll feel terrible for months once things dry up with your girl. Take that into VERY CAREFUL consideration when making your decision
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Cheers,
Garrett