Air carrier Captain reported misunderstanding of a CPDLC course reroute received in cruise and manually loading the clearance instead of using the load function resulted in a course deviation.

Narrative

En route from ZZZ1 to ZZZ we received a revised route clearance via CPDLC. The clearance was 'Load new route to ZZZZZ rest of route unchanged; due to weather.' The second page had dashes; then ZZZ2 XXX/XXY ZZZZZ./.ZZZ. The First Officer and I discussed it; loaded ZZZZZ in the LEGS 1 Page; and executed the route with LNAV engaged. We thought we were cleared directly to ZZZZZZ for weather buildups around the ZZZ2 XXX/XXY fix. After about 10 minutes; as I came back to flight intercom after coordinating with the flight attendants; the First Officer informed me ATC wanted us to fly to the ZZZ2 XXX/XXY fix and then ZZZZZ. I reprogrammed the FMC and executed the route. It was then; after further discussion; that we realized we should have flown to the ZZZ2 fix and then ZZZZZ. By then; the weather was dissipating; so there were no weather threats in the area. There also were no known traffic conflicts either. We then flew an uneventful arrival; approach; and landing into ZZZ.First; I had not seen a radial and DME fix in a CPDLC reroute in a long time; I believe. My expectation bias led me to think the re-route to ZZZZZ was for weather at that fix; and that led me and the First Officer to agree on direct ZZZZZ. But; as I discovered after we realized our error; if I had used the load function of CPDLC instead of the manual direct function; the ZZZ2 fix and ZZZZZ would have loaded in sequence. But because I misinterpreted the CPDLC message as the re-route was for weather around the ZZZ2 fix; that led me to my error. The First Officer and I discussed that next time we would query ATC in a similar situation; to make sure our interpretation was correct; plus the load function is best versus plugging the point(s) directly into the LEGS page (even though the abeam points; if used; would disappear). I am certain if ATC had verbally given us the en route change; we would have executed it with no issues; so this situation taught me a good lesson to adhere to our procedures and query ATC if there is any issue; plus to balance the written CPDLC reroute clearance with both of our expectations to make sure we comply with ATC's instructions.