I really didn’t understand the voting system from your brief description, so I checked with a (German language) source that is typically very trustworthy when it comes to the intricacies of voting systems (Wahlrecht.de) and found that … your description is somewhat incomplete.
So first, how does it work? (Paraphrasing from the Wahlrecht.de description)
A voter has two votes: one for a local candidate elected by a simple majority and one for a national list. (Voters not residing in Hungary only receive a national list vote.)
As expected, local candidates are elected by a simple majority; this fills 106 of the 199 seats in parliament.
The remaining 93 seats are distributed according to the national list vote shares using the d’Hondt method (also known as Jefferson’s method). However, not only the national list votes count:
- Any votes for non-winning local candidates are transferred entirely to their national list
- For the candidate winning a constituency, only the surplus votes are transferred to the national list.
This is actually what your example represents; if we assume your totals to be the local constituency total then party A would receive 999 list votes (they needed 3001 to win the constituency)
(The above is subject to the 5 % threshold you mentioned; I did not bother looking up whether the threshold applies to national list votes only or including the transferred votes. In most cases, it would not differ too significantly.)
Revisiting your example and assuming that each of the 106 constituencies voted exactly like that (meaning party A gains 106 seats of the constituencies) and also assuming that all over the country the national list votes are identical, my Excel file tells me that party A will win 142 seats (71 %) while party B wins 43 (22 %) and party C 14 (7 %). (Results like that are highly unlikely as rarely a party will win such a landslide all over the country; although Bavarian elections have resulted in all constituencies being held by CSU candidates.)
This is not a Mixed-Member Proportional representation (MMP) system but rather a Parallel Voting system. The outcome of the FPTP constituency seats has little to no bearing on how the national list seats are allocated. Similar systems exist e.g. in Japan, where the 465 seats in the House of Representatives are split into 289 single-member constituencies and 176 proportional representation seats. (The latter in Japan are not allocated nationwide but on a regional level.)
The Hungarian system includes a bonus to those parties who did less well in securing constituencies. In a pure FPTP system such as the British system, if one party scored 10000 votes in every constituency but the other 10001, the second would win all seats. In a simple Parallel Voting system as in Japan, they might also score 50 % of the proportional representation seats. In the Hungarian system, this effect is balanced out as the losing party can take 10000 votes per constituency into the national vote election but the winning party only 1, leading to a roughly 2:1 ratio in favour of the FPTP loser. This seems to strengthen the proportional aspect of the system.
However, the majority of seats are still allocated by FPTP constituencies so in essence securing relative majorities all across the country will likely remain more important.
The actual question was: Is this democratic?
The answer is a clear yes.
First of all, the formal requirements are present: every vote counts the same in the constituency it is cast in, everyone has (to the best of my knowledge) the right to vote and there is a real choice of candidates.
Second, the constituency winners are chosen by a clearly democratic process: first past the post. This is standard where only one position is open for election but where it is not considered important enough for an absolute majority (so a runoff election is not required). This also applies to the national list vote as the D’Hondt process, while systematically favouring large parties when it comes to residual seats, still represents a common quota system. (In most elections there are only minor differences between the results according to d’Hondt, Sainte-Laguë or other quota systems.)
The transfer of constituency losers votes (and surplus votes) actually makes the proportional block slightly more balancing imho, as not every vote on a losing candidate is lost. So those who voted for a candidate of the losing party are better represented in the national list vote which balances out the skewing of FPTP somewhat. But even without such a transfer (again: see Japan) this system would be considered democratic. And even without nationwide lists (see UK) this would be seen as democratic.
It is not a system of proportional representation like the one used in e.g. Germany. But there is no requirement for democratic elections to function according to proportional representation. All of these systems have their merits and disadvantages and deciding which one to use is an inherently political decision.