Yes, rival is definitely a promotion from boyfriend. That's when you exchange wristbands.
Also, the best thing about Abe is that he completely understands that he and Mihashi are the OTP of this series, and makes the "oh fuck" face a lot. Mihashi also is totally aware that they are the OTP, but on the other hand, doesn't know that it is not normal to be head over heels in love with your catcher after five seconds. But that's part of what makes him so cute.
"MIHASHI WE'RE IN PUBLIC GET OFF MY LAP." "But you're my catcher :<>"
Somebody make me a sexy Tajima icon.