I think this is really unlikely. It doesn't matter which of the claimants win in 68; the Principate and the Empire are strong enough that it's hard to see a setback that Rome couldn't recover from. The Batavians might dislodge Roman control in northern Germania for a little while but I can't really see them as a threat to Gaul in the longer term.
Is a Batavian rebellion likely to stay limited to just the Batavians though? (And especially if Vitellius pulls additional troops out of the Rhine to reinforce his army in Italy, which I think he will pretty much have to do to beat the Flavians.) The Trevari and Lingones might not join with the Batavians (as they did IOTL), in a Vitellius wins timeline as they seemed to have good relations with him, but conversely a Vitellian victory in Italy might see the Aeudi, Arveni, and Sequani join the revolt as all of those tribes had supported (and been rewarded by) Galba and thus had reason to fear Vitellius.
Titus is basically committed in Judea no matter what, and if there was a Parthian attempt on Syria Vespasian would come out of Alexandria. I guess in this TL we say, that happens, Vespasian loses in Syria along with Titus' legions -- then Primus and Mucianus have to turn around and attack from Asia Minor.
I don't see the Parthians attacking unless the Flavian armies in Italy have already been defeated. (Which is not impossible. The Vitellians had a chance to defeat the Flavians in detail thanks to Primus going off half cocked and advancing into Italy with only two legions rather than waiting for Mucianus' army to arrive, but the opportunity was lost due to the treachery of the Vitellian army commander Aulus Caecina Alienus. If Alienus isn't in command of the Vitellian army though or just decides he is better off sticking with Vitellius then you could see the Vitellians wipe out Primus before he gets reinforced, and at that point a fight between the Vitellians and Mucianus' army could go either way.
I could see Rome losing a chunk of Syria, probably Armenia becoming part of Parthia proper, assuming the worst case, but it's really hard to see Parthia taking more than that.
What would stop the Parthians from taking Cilicia and the Armenians from taking Pontus? Rome didn't really have any legions in Asia Minor at this point, so if Vespasian's army gets defeated in Syria, and the Vitellians and Mucianus' army wreck each other in Italy, then there isn't much to hold back the Parthians (at least until the Alans attack them in a couple of years.)
And Rome still has Italy, Gaul, the Spanish provinces, North Africa, Egypt, Greece, Asia...
Italy, Spain, and Asia yes.
Greece-yes though given that the Sarmatians will attack in force across the frozen Danube in 70 AD, Greece is not really a source of additional strength for Rome at this time but is rather another obligation to defend when Rome already has a lot of its plate.
Gaul-I'm not so sure about. As mentioned above I think there's a good chance that the Aeudi, Arveni, and Sequani will join the Batavian revolt, and if that happens Rome is in a lot of trouble in Gaul. (And will the Trevari and Lingones stay loyal to Rome if it looks like the Romans are on the run?)
Egypt-not sure about this one either. If the Flavians lose in Syria they are likely to retreat into Egypt and fortify the blazes out of it. The Roman world could then end up divided between a Vitellian controlled Italy and a Flavian controlled Egypt (which might leave both factions too weakened to unify the empire.)
North Africa-probably. Though if the Flavians manage to solidify their position in Egypt, they will probably then try to take Africa (with an eye to cutting Rome's grain supply), so Africa could become seriously contested.
So while I agree with you that a complete collapse of the Roman Empire is very unlikely at this point, I could see Rome losing significant territory in both Gaul and the east that it will have a very hard time reclaiming.