Everyone here seems to assume that the "Selbstausschaltung des Parlaments" still happens.
Okay, let's break this down. Dollfuß became Chancellor in May 1932.
The NSDAP under Hitler OTL wins the election in July 32 with some 37 odd percent.
In November another election happens in Germany, leaving the NSDAP with 33 odd percent.
Hitler then becomes Chancellor in January 33, and the German reorganization starts. Hindenburg then dies in August, leaving Hitler as Chancellor-President, or simply Führer.
Meanwhile in March 33 the Selbstausschltung happens.
Since the PoD states that Hitler does not come into power in 1932, I'll assume they did slightly worse in the 32 elections. That in turn means that with slightly more votes for the center and right wing parties, leading to some right mess. Probably a minority centre-right government with NSDAP tolerance. Considering such a government the fringe will continue to gain support - both NSDAP and Communists.
Then March happens. The Austrian railway workers, assumed to be socialists to the last man, strike once again. A vote is called on their demands. There is no relative stable right wing coalition that agitates for Austria to join Germany in Germany. Would all the right wing/german nationalists vote for the railway workers demands? With the intention to cause a crisis?
For the matter, there were 165 members of parliament since the 1930 election. 164 voted that day. If one more is missing or the missing one turns up?
Also: There might be an election called during that time. The Austrian government was in (constant) crisis and without the NSDAP winning in Germany there might be less fear among the CS to lose votes to them in an Austrian election.
Still, knowing the parties at the time: Christian-Socialists weren't democrats. Ideologically they wanted a "Stände" system, a return to a medieval balance, modernized. Some hereditary votes, some to the church and the rest to the population voted among the ones of the same vocation.
Neither was the SPÖ democratic. They very much were socialists, they weren't all that beholden to Moscow, but they were left enough that no communist party arose in numbers.
Among the remains? German nationalists, right wing nationalists, even the odd monarchist in irrelevant small numbers (aside from coalitions) - and certainly not democrats.
Faced with the chance of losing power (or gaining it for the matter), sooner or later someone was going to do something. It could be the relative bloodless coup of the CS - without Hitler and his NSDAP stirring in the background even the short civil war might not happen. It could however be a socialist uprising as well. Likely to not end well for them, but it could happen.
Without outsiders meddling I can't see a drawn out civil war however. And unless Germany goes Red I doubt that the socialists can get that much support into land locked Austria. Unlike the right wing, with Mussolini right on the border.
So yes, a right wing dictatorship is a likely possibility. How that ends is a different question. Without the Nazis in power in Germany a NSDAP putsch killing Dollfuß is less likely. I can't really tell how he would have ruled long term.
If you however consider OTL: under Schuschnigg they had already planed the first "vocational branches" to vote in summer 1938, a vote that never happened due to the Anschluss. It might end up a weird kind of partial democracy. No universal vote, a party structure in the background as "king maker" on the Ministerial and Chancellor posts, and relative free, but ultimately limited votes among vocational lines, ensuring CS domination.
Something that might grow more open or closed, depending on what happens in the wider world. Because preventing Hitler from taking power will cause very large butterflies.