Why did other German political parties disband so fast when Hitler was appointed chancellor?

Three steps to observe:

1. Hitler was given the chancellory
2. Election in 1933
3. Reichstag fire & Enabling decree

First the really unwanted elements were beaten up, imprisoned or just killed. Then a lot of the right-wingers saw their wishes and chances and did not switch sides, to the contrary, they just switched the membership card. Then, after eliminating most of the legal options for opposition some parties were prohibited and many party members of those further down on the list had a sudden loss of membership as well.

The election took place after the Nazis came to power on 30 January, when President Paul von Hindenburg appointed Hitler as Chancellor. The latter immediately urged the dissolution of the Reichstag and the calling of new elections. In early February, the Nazis "unleashed a campaign of violence and terror that dwarfed anything seen so far." Stormtroopers began attacking trade union and Communist Party (KPD) offices and the homes of left-wingers.

And then the enabling act, with regard to the Centre party:

With the passing of the Enabling Act the Centre Party had set in motion its own demise. As promised during the negotiations, a working committee chaired by Hitler and Kaas and supposed to inform about further legislative measures, met three times (31 March, 2 April and 7 April) without any major impact.

At that time, the Centre Party was weakened by massive defections by party members. Loyal party members, in particular civil servants, and other Catholic organisations were subject to increasing reprisals, despite Hitler's previous guarantees. The party was also hurt by a declaration of the German bishops that, while maintaining their opposition to Nazi ideology, modified the ban on cooperation with the new authorities.

The issue of the concordat prolonged Kaas' stay in Rome, leaving the party without a chairman, and on 5 May Kaas finally resigned from his post. The party now elected Brüning as chairman. The party adopted a tempered version of the leadership principle; pro-Centre papers now declared that the party's members, or "retinue", would fully submit itself to Brüning. It was not enough, however, to relieve the growing pressure that it and other parties faced in the wake of the process of Gleichschaltung. Prominent members were frequently arrested and beaten, and pro-Centre civil servants were fired. As the summer of 1933 wore on, several government officials—including Papen—demanded that the Centre either dissolve or be closed down by the government.

By July, the Centre was the only non-Nazi party that had not been browbeaten into dissolving itself (or had been banned outright, like the SPD). On 1 July, Papen and Kaas agreed that as part of the concordat, German priests would stay out of politics. Earlier, as part of negotiations, it was agreed that the party would dissolve as soon as the concordat had been concluded. As it turned out, the party dissolved on 5 July—much to the dismay of Cardinal Pacelli, who felt the party should at least have waited until after the conclusion of negotiations. The day after, the government issued a law declaring the NSDAP the only legally permitted party in the German state.

from Q: … the Nazis still only won around 44% of the vote. It would seem at this point, then, that there was still a significant number of Germans – perhaps close to half – who did not support the Nazis.

The communists were effectively structurally beheaded by that time and the fiercest opponents, even almost capable of offering armed resistance. While in that sorry state they still raked in 12.3% of votes, the social-democrats took 18.3%. Problem here is that only the SPD was against the nazis and actually for democracy. It's also quite the difference to see 44% of votes in staunch support of dictatorship tied to ony party and concluding that therefore 55% were opposed.

In terms of ordering the political spectrum you would have to count the right-wing DNVP dominated KSWR with 8% towards the nazi seats, the Bavarian People's Party with another 2% as well, and while you're already close to the needed 2/3 dominance majority the rest of the parties were really insignificant by that time.

In 1933 the army was full of sympathetic right-wingers, true. But to say that the nazis "controlled them" is far from the truth. To the contrary, the military elites were unsure of what to think of the Hitlerites and especially of the SA. By the end of 1933 the army was the only element left – short of a popular uprising – that could have stopped the fascists. But there were just no democrats to be found anywhere anymore. Also noteworthy is the fact that the Reichswehr was still at 115000 men. The SA by then had 2.9 million members.