can someone become a GM or any other type of master by playing on chess.com?


Decided to dig into the FIDE handbook to pinpoint the rule. The rulebook can be found here. Quotes of interest pasted below:
Chapter B01
0.3
The International FIDE titles shall be under the umbrella of the Qualification Commission, which is the final judging unit. The titles are:
0.31
Titles for over-the-board standard chess (as defined in the Laws of Chess), the judging unit being the QC:
Grandmaster (GM), International Master (IM), FIDE Master (FM), Candidate Master (CM), Woman Grandmaster (WGM), Woman International Master (WIM), Woman FIDE Master (WFM), Woman Candidate Master (WCM).

Interesting. I didn't even know that there were "Arena" titles. Unfortunately, these are not serious titles, and they seem to be primarily a way for the FIDE arena to earn extra money. The requirements and description can be found in the online arena or in this Wikipedia entry.
They may serve as goals for low-level players, but the titles unfortunately do not carry much weight at well. For instance, an AGM (Arena Grandmaster) less ELO than the first tier of OTB masters.